Combinatorial Problems and ExercisesThe aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified. |
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Contents
Spectra of graphs and random walks relations to | 9 |
Preface | 11 |
Reconstruction linegraphs the Reconstruction | 15 |
Copyright | |
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Common terms and phrases
1-factor of G 2-coloration 2-connected 3-regular a-critical adjacent automorphism group bipartite graph classes color combinatorial complete graph components of G connected graph Consider contradiction cycle cycle index defined degree at least denote the number digraph disjoint edge-disjoint edges of G eigenvalues eigenvector elements endpoints Euler trail exactly fc-coloration follows formula G contains G is connected graph G Hamiltonian circuits Hamiltonian path Hence hint hypergraph independent set induced subgraph induction hypothesis integers isomorphic joined length Let G Math matrix maximum independent set maximum matching Menger's theorem minimal monochromatic neighbors number of edges number of partitions obviously odd circuit odd number orientation path permutation planar planar graph points of degree points of G problem proves the assertion recurrence relation resulting graph satisfies sequence Similarly simple graph solution spanning tree strongly connected subgraph of G subset Suppose that G theorem triangle trivial vertex vertices