The notes that eventually became this book were written between
1977 and 1985 for the course called Constructive Combinatorics at
the University of Minnesota. This is a one-quarter (10 week) course
for upper level undergraduate students. The class usually consists
of mathematics and computer science majors, with an occasional
engineering student. Several graduate students in computer science
also attend. At Minnesota, Constructive Combinatorics is the third
quarter of a three quarter sequence. The fIrst quarter, Enumerative
Combinatorics, is at the level of the texts by Bogart [Bo], Brualdi
[Br], Liu [Li] or Tucker [Tu] and is a prerequisite for this
course. The second quarter, Graph Theory and Optimization, is not a
prerequisite. We assume that the students are familiar with the
techniques of enumeration: basic counting principles, generating
functions and inclusion/exclusion. This course evolved from a
course on combinatorial algorithms. That course contained a mixture
of graph algorithms, optimization and listing algorithms. The
computer assignments generally consisted of testing algorithms on
examples. While we felt that such material was useful and not
without mathematical content, we did not think that the course had
a coherent mathematical focus. Furthermore, much of it was being
taught, or could have been taught, elsewhere. Graph algorithms and
optimization, for instance, were inserted into the graph theory
course where they naturally belonged. The computer science
department already taught some of the material: the simpler
algorithms in a discrete mathematics course; effIciency of
algorithms in a more advanced course.
General
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