This volume constitutes the refereed proceedings of the 11th International Workshop on Combinatorial Image Analysis, IWCIA 2006, held in Berlin, June 2006. The book presents 34 revised full papers together with two invited papers, covering topics including combinatorial image analysis; grammars and models for analysis and recognition of scenes and images; combinatorial topology and geometry for images; digital geometry of curves and surfaces; algebraic approaches to image processing, and more.

Boundaries and Hulls of Euclidean Graphs: From Theory to Practice presents concepts and algorithms for finding convex, concave and polygon hulls of Euclidean graphs. It also includes some implementations, determining and comparing their complexities. Since the implementation is application-dependent, either centralized or distributed, some basic concepts of the centralized and distributed versions are reviewed. Theoreticians will find a presentation of different algorithms together with an evaluation of their complexity and their utilities, as well as their field of application. Practitioners will find some practical and real-world situations in which the presented algorithms can be used.

Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a uniquely intuitive approach to the subject: it presents hundreds of extreme value problems, examples, and solutions primarily through Euclidean geometry. Written by a team of established mathematicians and professors, this work draws on the authors' experience in the classroom and as Olympiad coaches. By exposing readers to a wealth of creative problem-solving approaches, the text communicates not only geometry but also algebra, calculus, and topology. Ideal for use at the junior and senior undergraduate level, as well as in enrichment programs and Olympiad training for advanced high school students, this book's breadth and depth will appeal to a wide audience, from secondary school teachers and pupils to graduate students, professional mathematicians, and puzzle enthusiasts.

50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC). The conference is noted for the dissemination and stimulation of research, while fostering collaborations among mathematical scientists at all stages of their careers. The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering. Readers will discover the breadth and depth of the presentations at the SEICCGTC, as well as current research in combinatorics, graph theory and computer science. Features: Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys Surveys highlight open questions to inspire further research Chapters are written by experts in their fields Extensive bibliographies are provided at the end of each chapter

This volume contains the papers presented at the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2005) and the 9th International Workshop on Randomization and Computation(RANDOM2005), whichtookplaceconcurrentlyattheUniversity of California in Berkeley, on August 22-24, 2005. APPROX focuses on algori- mic and complexity issues surrounding the development of e?cient approximate solutions to computationally hard problems, and APPROX 2005 was the eighth in the series after Aalborg (1998), Berkeley (1999), Saarbru ]cken (2000), Ber- ley (2001), Rome (2002), Princeton(2003), and Cambridge(2004).RANDOM is concerned with applications of randomness to computational and combinatorial problems, and RANDOM 2005 was the ninth workshop in the series foll- ing Bologna (1997), Barcelona (1998), Berkeley(1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), and Cambridge (2004). Topics of interest for APPROX and RANDOM are: design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, geometric problems, game theory and applications, network designandrouting, packingand covering, scheduling, designandanalysisofr- domized algorithms, randomized complexity theory, pseudorandomness and - randomization, random combinatorialstructures, randomwalks/Markovchains, expander graphs and randomness extractors, probabilistic proof systems, r- dom projections and embeddings, error-correcting codes, average-case analysis, property testing, computational learning theory, and other applications of - proximation and randomness. The volume contains 20 contributed papers selected by the APPROX P- gram Committee out of 50 submissions, and 21 contributed papers selected by the RANDOM Program Committee out of 51 submis

Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers' appreciation of mathematics. This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers' attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy. Highlights: Features fascinating historical context to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text's narrative style is that of a popular book, not a dry textbook Includes the work of many living mathematicians Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses Contains many open problems Profusely illustrated

This volume consists of the refereed papers presented at the Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory (IJCCGGT 2003), held on September 13 16, 2003 at ITB, Bandung, Indonesia. This conf- ence can also be considered as a series of the Japan Conference on Discrete and Computational Geometry (JCDCG), which has been held annually since 1997. The ?rst ?ve conferences of the series were held in Tokyo, Japan, the sixth in Manila, the Philippines, in 2001, and the seventh in Tokyo, Japan in 2002. The proceedings of JCDCG 1998, JCDCG 2000 and JCDCG 2002 were p- lished by Springer as part of the series Lecture Notes in Computer Science: LNCS volumes 1763, 2098 and 2866, respectively. The proceedings of JCDCG 2001 were also published by Springer as a special issue of the journal Graphs and Combinatorics, Vol. 18, No. 4, 2002. TheorganizersaregratefultotheDepartmentofMathematics, InstitutTek- logi Bandung (ITB) and Tokai University for sponsoring the conference. We also thank all program committee members and referees for their excellent work. Our big thanks to the principal speakers: Hajo Broersma, Mikio Kano, Janos Pach andJorgeUrrutia.Finally, ourthanksalsogoestoallourcolleagueswhoworked hard to make the conference enjoyable and successful. August 2004 Jin Akiyama Edy Tri Baskoro Mikio Kano Organization The Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory (IJCCGGT) 2003 was organized by the Department of Mathematics, InstitutTeknologiBandung(ITB)IndonesiaandRIED, TokaiUniversity, Japan

This volume presents the proceedings of the 10th International Workshop on Combinatorial Image Analysis, held December 1 3, 2004, in Auckland, New Zealand. Prior meetings took place in Paris (France, 1991), Ube (Japan, 1992), Washington DC (USA, 1994), Lyon (France, 1995), Hiroshima (Japan, 1997), Madras (India, 1999), Caen (France, 2000), Philadelphia (USA, 2001), and - lermo (Italy, 2003). For this workshop we received 86 submitted papers from 23 countries. Each paper was evaluated by at least two independent referees. We selected 55 papers for the conference. Three invited lectures by Vladimir Kovalevsky (Berlin), Akira Nakamura (Hiroshima), and Maurice Nivat (Paris) completed the program. Conference papers are presented in this volume under the following topical part titles: discrete tomography (3 papers), combinatorics and computational models (6), combinatorial algorithms (6), combinatorial mathematics (4), d- ital topology (7), digital geometry (7), approximation of digital sets by curves and surfaces (5), algebraic approaches (5), fuzzy image analysis (2), image s- mentation (6), and matching and recognition (7). These subjects are dealt with in the context of digital image analysis or computer vision."

a ~Networka (TM) is a heavily overloaded term, so that a ~network analysisa (TM) means different things to different people. Specific forms of network analysis are used in the study of diverse structures such as the Internet, interlocking directorates, transportation systems, epidemic spreading, metabolic pathways, the Web graph, electrical circuits, project plans, and so on. There is, however, a broad methodological foundation which is quickly becoming a prerequisite for researchers and practitioners working with network models.

From a computer science perspective, network analysis is applied graph theory. Unlike standard graph theory books, the content of this book is organized according to methods for specific levels of analysis (element, group, network) rather than abstract concepts like paths, matchings, or spanning subgraphs. Its topics therefore range from vertex centrality to graph clustering and the evolution of scale-free networks.

In 15 coherent chapters, this monograph-like tutorial book introduces and surveys the concepts and methods that drive network analysis, and is thus the first book to do so from a methodological perspective independent of specific application areas.

Thisvolumeconsistsofpapersselectedfromthe presentationsgivenatthe Int- national Workshop and Symposium on "Applications of Graph Transformation with Industrial Relevance" (AGTIVE 2003). The papers underwent up to two additional reviews. This volume contains the revised versions of these papers. AGTIVE2003wasthesecondeventoftheGraphTransformationcommunity. The aim of AGTIVE is to unite people from research and industry interested in the application of Graph Transformation to practical problems. The ?rst wo- shoptookplaceatKerkrade,TheNetherlands.Theproceedingsappearedasvol. 1779ofSpringer-Verlags'sLectureNotesinComputerScienceseries.Thissecond workshop, AGTIVE 2003, was held in historic Charlottesville, Virginia, USA. Graphs constitute well-known, well-understood, and frequently used means to depict networks of related items in di?erent application domains. Various typesofgraphtransformationapproaches- alsocalledgraphgrammarsorgraph rewriting systems - have been proposed to specify, recognize, inspect, modify, anddisplaycertainclassesofgraphsrepresentingstructuresofdi?erentdomains. Research activities based on Graph Transformations (GT for short) cons- tute a well-established scienti?c discipline within Computer Science. The int- national GT research community is quite active and has organized international workshops and the conference ICGT 2002. The proceedings of these events, a three volume handbook on GT, and books on speci?c approaches as well as big application projects give a good documentation about research in the GT ?eld (see the list at the end of the proceedings). The intention of all these activities has been (1) to bring together the - ternational community in a viable scienti?c discussion, (2) to integrate di?erent approaches, and (3) to build a bridge between theory and practice.

A complete, self-contained introduction to a powerful and resurging mathematical discipline … Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Tóth, Rogers, and Erd???s. Nearly half the results presented in this book were discovered over the past twenty years, and most have never before appeared in any monograph. Combinatorial Geometry will be of particular interest to mathematicians, computer scientists, physicists, and materials scientists interested in computational geometry, robotics, scene analysis, and computer-aided design. It is also a superb textbook, complete with end-of-chapter problems and hints to their solutions that help students clarify their understanding and test their mastery of the material. Topics covered include:

• Geometric number theory
• Packing and covering with congruent convex disks
• Extremal graph and hypergraph theory
• Distribution of distances among finitely many points
• Epsilon-nets and Vapnik—Chervonenkis dimension
• Geometric graph theory
• Geometric discrepancy theory
• And much more

This self-contained book examines results on transfinite graphs and networks achieved through a continuing research effort during the past several years. These new results, covering the mathematical theory of electrical circuits, are different from those presented in two previously published books by the author, Transfiniteness for Graphs, Electrical Networks, and Random Walks and Pristine Transfinite Graphs and Permissive Electrical Networks.

Two initial chapters present the preliminary theory summarizing all essential ideas needed for the book and will relieve the reader from any need to consult those prior books. Subsequent chapters are devoted entirely to novel results and cover:

* Connectedness ideas---considerably more complicated for transfinite graphs as compared to those of finite or conventionally infinite graphs----and their relationship to hypergraphs

* Distance ideas---which play an important role in the theory of finite graphs---and their extension to transfinite graphs with more complications, such as the replacement of natural-number distances by ordinal-number distances

* Nontransitivity of path-based connectedness alleviated by replacing paths with walks, leading to a more powerful theory for transfinite graphs and networks

Additional features include:

* The use of nonstandard analysis in novel ways that leads to several entirely new results concerning hyperreal operating points for transfinite networks and hyperreal transients on transfinite transmission lines; this use of hyperreals encompasses for the first time transfinite networks and transmission lines containing inductances and capacitances, in addition to resistances

* A useful appendix with concepts from nonstandard analysis used in the book

* May serve as a reference text or as a graduate-level textbook in courses or seminars

Graphs and Networks: Transfinite and Nonstandard will appeal to a diverse readership, including graduate students, electrical engineers, mathematicians, and physicists working on infinite electrical networks. Moreover, the growing and presently substantial number of mathematicians working in nonstandard analysis may well be attracted by the novel application of the analysis employed in the work.

ISBN 0-8176-4292-7

Graph Searching Games and Probabilistic Methods is the first book that focuses on the intersection of graph searching games and probabilistic methods. The book explores various applications of these powerful mathematical tools to games and processes such as Cops and Robbers, Zombie and Survivors, and Firefighting. Written in an engaging style, the book is accessible to a wide audience including mathematicians and computer scientists. Readers will find that the book provides state-of-the-art results, techniques, and directions in graph searching games, especially from the point of view of probabilistic methods. The authors describe three directions while providing numerous examples, which include: * Playing a deterministic game on a random board. * Players making random moves. * Probabilistic methods used to analyze a deterministic game.

ICGT 2004 was the 2nd International Conference on Graph Transformation, following the ?rst one in Barcelona (2002), and a series of six international workshops on graph grammars with applications in computer science between 1978 and 1998. ICGT 2004 was held in Rome (Italy), Sept. 29 Oct. 1, 2004 under the auspices of the European Association for Theoretical Computer S- ence (EATCS), the European Association of Software Science and Technology (EASST), and the IFIP WG 1.3, Foundations of Systems Speci?cation. The scope of the conference concerned graphical structures of various kinds (like graphs, diagrams, visual sentences and others) that are useful when - scribing complex structures and systems in a direct and intuitive way. These structures are often augmented with formalisms that add to the static descr- tion a further dimension, allowing for the modelling of the evolution of systems via all kinds of transformations of such graphical structures. The ?eld of graph transformation is concerned with the theory, applications, and implementation issues of such formalisms. The theory is strongly related to areas such as graph theory and graph - gorithms, formal language and parsing theory, the theory of concurrent and distributed systems, formal speci?cation and veri?cation, logic, and semantics. The application areas include all those ?elds of computer science, information processing, engineering, andthe naturalsciences wherestatic anddynamicm- elling using graphical structures and graph transformations, respectively, play important roles. In many of these areas tools based on graph transformation technology have been implemented and used."

Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.

Rosemary Bailey covers in this study the mathematics of association schemes--an area lying between pure mathematics and statistics that relates to the optimal design of scientific experiments. The book is accessible to mathematicians as well as statisticians. Arising from a graduate course taught by the author, it appeals to students as well as researchers as a valuable reference work from which to learn about the statistical/combinatorial aspects of their work.

Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing number of courses in schools and universities. Graphs and Applications is based on a highly successful Open University course and the authors have paid particular attention to the presentation, clarity and arrangement of the material, making it ideally suited for independent study and classroom use. An important part of learning graph theory is problem solving; for this reason large numbers of examples, problems (with full solutions) and exercises (without solutions) are included.Accompanying the book is a CD-ROM comprising a Graphs Database, containing all the simple unlabelled graphs with up to seven vertices, and a Graphs Editor that enables students to construct and manipulate graphs. Both the Database and Editor are simple to use and allow students to investigate graphs with ease. Computing Notes and suggested activities are provided.

Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.

This book constitutes the thoroughly refereed post-proceedings of the 10th International Symposium on Graph Drawing, GD 2002, held in Irvine, CA, USA, in August 2002.The 24 revised full papers, 9 short papers, and 7 software demonstrations presented together with a report on the GD 2002 graph drawing contest were carefully reviewed and selected from a total of 48 regular paper submissions. All current aspects of graph drawing are addressed.

New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.

This book constitutes the refereed proceedings of the First International Conference on Graph Transformations, ICGT 2002, held in Barcelona, Spain in October 2002.The 26 revised full papers presented were carefully reviewed and selected by the program committe. Also included are abstracts of 3 invited papers, a tutorial, the extended abstract of a tutorial, and 5 reports of workshops held in conjunction with ICGT. The papers deal with various graphical structures that are useful to describe complex systems and computational structures, like graphs, diagrams, visual sentences, and others. Graph transformations are stongly related to graph theory, graph algorithms, formal language and parsing theory, the theory of concurrent and distributed systems, formal specification and verification, and logic and semantics.

This book constitutes the refereed proceedings of the 8th Annual International Computing and Combinatorics Conference, COCOON 2002, held in Singapore in August 2002.The 60 revised full papers presented together with three invited contributions were carefully reviewed and selected from 106 submissions. The papers are organized in topical sections on complexity theory, discrete algorithms, computational biology and learning theory, radio networks, automata and formal languages, Internet networks, computational geometry, combinatorial optimization, and quantum computing.

This volume contains the proceedings of the NATO Advanced Study Institute "Symmetric Functions 2001: Surveys of Developments and Per- spectives", held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, during the two weeks 25 June - 6 July 2001. The objective of the ASI was to survey recent developments and outline research perspectives in various fields, for which the fundamental questions can be stated in the language of symmetric functions (along the way emphasizing interdisciplinary connections). The instructional goals of the event determined its format: the ASI consisted of about a dozen mini-courses. Seven of them served as a basis for the papers comprising the current volume. The ASI lecturers were: Persi Diaconis, William Fulton, Mark Haiman, Phil Hanlon, Alexander Klyachko, Bernard Leclerc, Ian G. Macdonald, Masatoshi Noumi, Andrei Okounkov, Grigori Olshanski, Eric Opdam, Ana- toly Vershik, and Andrei Zelevinsky. The organizing committee consisted of Phil Hanlon, Ian Macdonald, Andrei 0 kounkov, G rigori 0 lshanski (co-director), and myself ( co-director). The original ASI co-director Sergei Kerov, who was instrumental in determining the format and scope of the event, selection of speakers, and drafting the initial grant proposal, died in July 2000. Kerov's mathemat- ical ideas strongly influenced the field, and were presented at length in a number of ASI lectures. A special afternoon session on Monday, July 2, was dedicated to his memory.

This book constitutes the refereed proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching, CPM 2002, held in Fukuoka, Japan, in July 2002.The 21 revised full papers presented together with two invited contributions were carefully reviewed and selected from 37 submissions. The papers are devoted to current theoretical and computational aspects of searching and matching strings and more complicated patterns such as trees, regular expressions, graphs, point sets, and arrays. Among the application fields are the World Wide Web, computational biology, computer vision, multimedia, information retrieval, data compression, and pattern recognition.

The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.