Aspects of Combinatorics: A Wide-ranging IntroductionCombinatorics is a broad and important area of mathematics, and this textbook provides the beginner with the ideal introduction to many of the different aspects of the subject. |
Contents
The binomial coefficients | 1 |
How many trees? | 13 |
The marriage theorem | 25 |
Three basic principles | 36 |
Latin squares | 50 |
The first theorem of graph theory | 71 |
Edgecolourings | 81 |
Harems and tournaments | 91 |
Rook polynomials | 138 |
Planar graphs | 151 |
Mapcolourings | 166 |
Designs and codes | 179 |
Ramsey theory | 201 |
Hints for exercises | 224 |
Answers to exercises | 249 |
| 262 | |
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Common terms and phrases
A₁ assume B₁ binomial coefficients bipartite graph C₁ chapter chromatic polynomial codewords coefficient coloured red column complete graph connected graph consider convex cubic map d₁ deduce e₁ edge of G edge-colouring Eulerian path example exercise exist finite projective plane follows four colours G₁ G₂ girls give given graph G graph theory Hall's theorem Hamiltonian cycle Hence highest vertex degree illustrated incidence matrix induction hypothesis integer joined k₁ knows boys L₁ Latin rectangle least Let G minimum number multinomial coefficients mutually orthogonal n₁ number of edges number of vertices odd number pair pigeon-hole planar graph planar representation plane of order players positive integer precisely previous theorem proof Ramsey number Ramsey theory Ramsey's theorem recurrence relation red or green rook polynomial scores Show Solution three colours three-element subsets tournament transversal V₁ V₂ vertex degree vertex of degree vertex-colouring