For courses in undergraduate Combinatorics. Many new detailed applications are covered, including material on list colourings, expanding discussion of scheduling legislative committees, material on DNA sequence alignment, and material on cryptography. *NEW Section dealing with stable marriages and their many modern applications, including the assignment of interns to hospitals, dynamic labour markets, and strategic behaviour. *A mix of difficulty in topics with careful annotation that makes it possible to use this book in a variety of courses. *Treatment of applications as major topics of their own rather than as isolated examples. *Use of real applications from the current literature and the extensive modern literature citations. *Problem-solving through a variety of exercises that test routine ideas, introduce new concepts and applications, or attempt to challenge the reader to use the combinatorial techniques developed.
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The Basic Tools of Combinatorics
Introduction to Graph Theory
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A)-design algorithm applications assignment binary relation bipartite graph bit strings block Burnside's Lemma called cells Chapter chromatic polynomial circuit codewords coefficient colors combinatorial consider corresponding count the number defined digits digraph directed network elements encode Equation equivalence classes errors eulerian closed eulerian path exactly Example EXERCISES FOR SECTION Find the number finite flow given gives graph coloring graph G graph of Figure graph theory Hadamard Hadamard matrix hamiltonian Hence integer labeled least linear Math Mathematical maximum minimum multigraph Note number of distinct obtained optimal ordinary generating function pair path permutation player polynomial possible probability projective plane proof of Theorem properties recurrence Repeat Exercise result RNA chain sequence Show solution spanning tree stable marriage problem stable matchings Steiner triple system Step strict partial order strings of length strongly connected subgraph subsets switching functions Table vertex weak orders