A mathematical gem–freshly cleaned and polished

This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.

Features retained from the first edition:

• Lively and engaging writing style
• Timely and appropriate examples
• Numerous well-chosen exercises
• Flexible modular format
• Optional sections and appendices

Highlights of Second Edition enhancements:

• Smoothed and polished exposition, with a sharpened focus on key ideas
• Expanded discussion of linear codes
• New optional section on algorithms
• Greatly expanded hints and answers section
• Many new exercises and examples

A lively invitation to the flavor, elegance, and power of graph theory

This mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. An award-winning teacher, Russ Merris has crafted a book designed to attract and engage through its spirited exposition, a rich assortment of well-chosen exercises, and a selection of topics that emphasizes the kinds of things that can be manipulated, counted, and pictured. Intended neither to be a comprehensive overview nor an encyclopedic reference, this focused treatment goes deeply enough into a sufficiently wide variety of topics to illustrate the flavor, elegance, and power of graph theory.

Another unique feature of the book is its user-friendly modular format. Following a basic foundation in Chapters 1–3, the remainder of the book is organized into four strands that can be explored independently of each other. These strands center, respectively, around matching theory; planar graphs and hamiltonian cycles; topics involving chordal graphs and oriented graphs that naturally emerge from recent developments in the theory of graphic sequences; and an edge coloring strand that embraces both Ramsey theory and a self-contained introduction to Pólya’s enumeration of nonisomorphic graphs. In the edge coloring strand, the reader is presumed to be familiar with the disjoint cycle factorization of a permutation. Otherwise, all prerequisites for the book can be found in a standard sophomore course in linear algebra.

The independence of strands also makes Graph Theory an excellent resource for mathematicians who require access to specific topics without wanting to read an entire book on the subject.

I was sitting at home one day doodling this flower. She had such a pretty look to her that I had to add a face, Once I did this- it was like she came to life as a character. My mother loved her so much that I made her a full length picture of her. As a character, she sat on my shelf for 3 years. I knew that God had a plan for this character, I just had to wait. As I was driving home one day- the story unfolded in my mind. I, then drew a layout of how a flower grows from a seed to a flower, The story of a mustard seed popped in my mind and it was then I knew... The cycle of a seed is the same as a person's faith. Once it is planted, it just needs time And nurturing.

I named this book, "Honeycomb Thoughts" because I believe that our mind is like a real honeycomb. It has wax pockets full of wonderful thoughts, images, pictures of the past, and everything you have ever filed away in your mind. When we write we are pouring out this divine honey that we can share with others. In my opinion, that is real poetry.