## Graph ColouringsNine papers on graph colourings, presented by speakers at a one-day meeting at the Open University in December 1988. The topics presented have been chosen to cover as wide a field as possible within the area of graph colourings. Each paper contains a cetain amount of survey material to put the results of the paper into perspective, as well as a discussion of new results. It is not the aim of this book to present a succession of highly technical research papers which would be better in a specialized journal. |

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### Contents

Introduction | 1 |

FRED HOLROYD and FEODOR LOUPEKINE | 37 |

AMANDA CHETWYND | 65 |

Copyright | |

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### Common terms and phrases

adjacent applications Behzad bipartite graph Bollobas chromatic polynomial class of graphs colour class colour the vertices colouring of G Combinatorial Theory complete graph component connected graph contains corresponding critical graphs cubic graph deﬁne denote diagram Discrete Math disjoint edge colourings edges of G equivalent faces ﬁnd ﬁnite ﬁrst four colour problem four colour theorem graph colouring graph G Graph Theory harmonious colouring incident induced inequality integer invariant k-chromatic graph k-colouring Kostochka least Lemma Let G line-distinguishing list colouring London Math m,d)*-colourable Mathematics maximum degree moves of type multigraph Nonlinear partial differential number of colours number of edges number of vertices outerplanar partial differential equations path planar graph plane Proc proof proved random graphs References regular graphs Reidemeister moves satisﬁes subcontraction subgraph of G sufﬁcient Suppose Theorem 2.1 Toft total chromatic number total colouring triangle-free upper bound vertex colouring vertex-set vertices of G W. T. Tutte