Graph Theory: An Introductory CourseFrom the reviews: "Béla Bollobás 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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Common terms and phrases
1-factor a.e. graph a₁ a₂ adjacency matrix algorithm automorphism group bipartite graph C₁(G Cayley diagram Chapter chromatic number complete graph components connected graph Corollary d₁ d₂ defined degree sequence denote directed graph edge coloured edge xy edges of G eigenvalue electrical network Euler trail ex(n exactly Exercise extremal graph Figure finite flow function G contains G₁ G₂ given graph contains graph G graph of order graph theory H₂ Hamilton cycle Hamilton path implies independent edges induction inequality integer isomorphic joined k-colouring least Lemma Let G Math max-flow min-cut theorem maximal number Menger's theorem minimal natural numbers number of edges obtained P(edge permutation planar plane graph polynomial problem Prove Ramsey random graphs rectangle result Schreier diagram Show space spanning tree square strongly regular graph subsets T₁ V₁ V₂ vector vertex classes vertex set x₁