Author	Bollobรกs, Bรฉla. author
Title	Graph Theory [electronic resource] : An Introductory Course / by Bรฉla Bollobรกs
Imprint	New York, NY : Springer New York, 1979
Connect to	http://dx.doi.org/10.1007/978-1-4612-9967-7
Descript	X, 180p. 80 illus. online resource

From the reviews: "Bรฉla Bollobรกs 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

I Fundamentals -- 1. Definitions -- 2. Paths, Cycles and Trees -- 3. Hamilton Cycles and Euler Circuits -- 4. Planar Graphs -- 5. An Application of Euler Trails to Algebra -- Exercises -- Notes -- II Electrical Networks -- 1. Graphs and Electrical Networks -- 2. Squaring the Square -- 3. Vector Spaces and Matrices Associated with Graphs -- Exercises -- Notes -- III Flows, Connectivity and Matching -- 1. Flows in Directed Graphs -- 2. Connectivity and Mengerโs Theorem -- 3. Matching -- 4. Tutteโs 1-Factor Theorem -- Exercises -- Notes -- IV Extremal Problems -- 1. Paths and Cycles -- 2. Complete Subgraphs -- 3. Hamilton Paths and Cycles -- 4. The Structure of Graphs -- Exercises -- Notes -- V Colouring -- 1. Vertex Colouring -- 2. Edge Colouring -- 3. Graphs on Surfaces -- Exercises -- Notes -- VI Ramsey Theory -- 1. The Fundamental Ramsey Theorems -- 2. Monochromatic Subgraphs -- 3. Ramsey Theorems in Algebra and Geometry -- 4. Subsequences -- Exercises -- Notes -- VII Random Graphs -- 1. Complete Subgraphs and Ramsey NumbersโThe Use of the Expectation -- 2. Girth and Chromatic NumberโAltering a Random Graph -- 3. Simple Properties of Almost All GraphsโThe Basic Use of Probability -- 4. Almost Determined VariablesโThe Use of the Variance -- 5. Hamilton CyclesโThe Use of Graph Theoretic Tools -- Exercises -- Notes -- VIII Graphs and Groups -- 1. Cayley and Schreier Diagrams -- 2. Applications of the Adjacency Matrix -- 3. Enumeration and Pรณlyaโs Theorem -- Exercises -- Notes -- Index of Symbols

1. Mathematics
2. Combinatorics
3. Mathematics
4. Combinatorics