## Advances in graph theory |

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### Contents

Benzaken and P L Hammer Linear separation of dominating sets | 1 |

Berge Regularisable graphs | 11 |

J C Bermond Hamiltonian decompositions of graphs directed graphs | 21 |

Copyright | |

18 other sections not shown

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### Common terms and phrases

1-factor 2-connected adjacent admissible lifting arises from G assume belongs bicycles chord cocycle colour complete graph conjecture connected components connected graph consider contradiction Corollary countable critical graphs decomposed defined denote disjoint domishold graph double edges edges of G elements end-vertices Erdos exists follows graph G Graphen Hamilton circuit hamiltonian circuits hamiltonian cycles hamiltonian decomposition hamiltonian paths Hence holds hypergraph implies incident induced subgraph inductive hypothesis inequality infinite least Lemma Let G lifting of G limit ordinal longest path loops Math matrix matroid maximal multigraph non-adjacent North-Holland Publishing Company number of edges number of hamiltonian number of vertices ordinal orthogonal pair partition percolation principal cycle proof of Theorem properties Proposition proved pseudograph queue regular graph regularisable result satisfying sequence set of vertices simplicial decomposition subgraph of G subset successor ordinal Suppose Theorem 2.1 u-critical valency vertex set vertices of G W.T. Tutte