## Graph theory: an introductory courseFrom the reviews: "Bčla Bollobās introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1 |

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### Contents

Chapter | 1 |

Hamilton Cycles and Euler Circuits | 11 |

An Application of Euler Trails to Algebra | 19 |

Copyright | |

13 other sections not shown

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### Common terms and phrases

1-factor a.e. graph adjacency matrix Algebra algorithm automorphism group bipartite graph Cayley diagram Chapter chromatic number complete graph components connected graph Corollary Deduce defined degree sequence denote directed graph edge coloured edge xy edges of G eigenvalue electrical network elements Euler trail ex(n exactly Exercise extremal graph Figure finite flow function G contains given graph contains graph G graph of order graph theory Hamilton cycle Hamilton path Hence implies independent edges induction inequality infinite set integer isomorphic joined least Lemma Let G Math max-flow min-cut theorem maximal number Menger's theorem minimal natural numbers number of edges number of vertices obtained P(edge permutation planar plane graph polynomial problem Prove Ramsey random graphs rectangle result Schreier diagram Show simple space spanning tree square strongly regular graph subgraph of G subsets Suppose vector vertex classes vertex set xu x2