## Decompositions of GraphsThis nice text (twenty years in the writing, published posthumously) would serve well to introduce graduate students (those who can afford it ) to a rich and important class of graph-theoretic problems and concepts. Fifteen short chapters (under three broad topical heads), to each of which are attac |

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### Contents

Section 1 | 3 |

Section 2 | 15 |

Section 3 | 19 |

Section 4 | 25 |

Section 5 | 47 |

Section 6 | 49 |

Section 7 | 57 |

Section 8 | 77 |

Section 12 | 117 |

Section 13 | 129 |

Section 14 | 133 |

Section 15 | 141 |

Section 16 | 165 |

Section 17 | 175 |

Section 18 | 185 |

Section 19 | 189 |

### Common terms and phrases

1-factor 4-regular A-fold a-labelling A)-design adjacent affine plane arbitrary automorphism Bermond and Sotteau blocks called cardinality chromatic number Colbourn colouring Combinatorial complementary graphs complete bipartite graph complete graph complete m-partite conjecture construct contains Corollary corresponding cyclic decomposition decom decomposable decompositions of complete decompositions of graphs defined denote digraph divisibility condition edges of length elements equivalent exactly example exists finite graph G and G Graceful Graphs graph decompositions graph G graph of order Graph Theory Hamiltonian cycles Hamiltonian decomposition Hamiltonian paths Hanani Harary Hell and Rosa Huang and Rosa hypergraph inequality integers isomorphic factors Kotzig labelling Lemma Let G Mathematics Mathon Nash-Williams non-isomorphic obtained Obviously orthogonal permutation plane of order positive integers problem Proc projective plane Proof proved regular graph resolvable resp self-complementary graph semiwalk simple graphs Steiner triple systems sufficient symmetric Theorem tonian tournaments triangles undirected graph vertex vertex-set Zelinka

### Popular passages

Page 231 - The number of open chains of length three and the parity of the number of open chains of length k In self-complementary graphs.

Page 208 - An application of the solution of Kirkman's schoolgirl problem: the decomposition of the symmetric oriented complete graph into 3-circuits, Discrete Math.

Page 233 - C. Huang. Another class of balanced graph designs: balanced circuit designs. Discrete Math. 12 (1975): 269-293. 69. J. Schönheim. Partition of the edges of the complete directed graph into 4-cycles. Discrete Math. 11 (1975): 67-70, 70. D. Sotteau. Decompositions of Km,„ (Kż „) into cycles (circuits) of length 2k.