## 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. |

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### 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

arithmetic progression assume binomial coefficients bipartite graph boxes chapter chromatic polynomial codewords coloured red complete graph connected graph consider consists convex convex polygon cubic map deduce deleting edge of G edge-colouring Eulerian path exercise face finite projective plane follows four colours girls give given graph G graph theory Hall's theorem Hamiltonian cycle Hence highest vertex degree illustrated incidence matrix induction hypothesis joined knows boys Latin rectangle least Let G minimum number multinomial coefficient n x n Latin squares non-challenging rooks number of different number of edges number of vertices odd number orthogonal n x n Latin pair pigeon-hole planar graph planar representation plane of order players points positive integer precisely previous theorem Ramsey number Ramsey theory Ramsey's theorem recurrence relation red or green rook polynomial scores shown Solution subgraph Theorem Let three colours three-element subsets tournament transversal vertex of degree vertex-colouring