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A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory

Miklós Bóna
World Scientific
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
, on

See our review of the second edition and our short note on the third edition.

There seem to be no major changes to the fourth edition. (It ain't broke…)There are some extra examples, new exercises, and for each chapter the author has provided "quick check" exercises at the end of each chapter. This is still one of the best introductions to combinatorics.

Fernando Q. Gouvêa is the editor of MAA Reviews.

  • Basic Methods:
    • Seven is More Than Six. The Pigeon-Hole Principle
    • One Step at a Time. The Method of Mathematical Induction
  • Enumerative Combinatorics:
    • There are a Lot of Them. Elementary Counting Problems
    • No Matter How You Slice It. The Binomial Theorem and Related Identities
    • Divide and Conquer. Partitions
    • Not So Vicious Cycles. Cycles in Permutations
    • You Shall Not Overcount. The Sieve
    • A Function is Worth Many Numbers. Generating Functions
  • Graph Theory:
    • Dots and Lines. The Origins of Graph Theory
    • Staying Connected. Trees
    • Finding a Good Match. Coloring and Matching
    • Do Not Cross. Planar Graphs
  • Horizons:
    • Does It Clique? Ramsey Theory
    • So Hard to Avoid. Subsequence Conditions on Permutations
    • Who Knows What It Looks Like, But It Exists. The Probabilistic Method
    • At Least Some Order. Partial Orders and Lattices
    • As Evenly as Possible. Block Designs and Error Correcting Codes
    • Are They Really Different? Counting Unlabeled Structures
    • The Sooner the Better. Combinatorial Algorithms
    • Does Many Mean More Than One? Computational Complexity