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Lecture Notes on GRAPH THEORY

Lecture Notes onGRAPH THEORYTero HarjuDepartment of MathematicsUniversity of TurkuFIN-20014 Turku, Finlande-mail: 2011 Contents1 introduction .. Graphs and their plane figures .. Subgraphs .. Paths and cycles .. 112 Connectivity of Graphs.. Bipartite graphs and trees .. Connectivity .. 233 Tours and Matchings.. Eulerian graphs .. Hamiltonian graphs .. Matchings .. 354 Colourings.. Edge colourings .. Ramsey THEORY .. Vertex colourings .. 535 Graphs on Surfaces.. Planar graphs .. Colouring planar graphs .. Genus of a GRAPH .. 766 Directed Graphs.. Digraphs.. Network Flows .. 90 Index.. 971 IntroductionGraph THEORY may be said to have its begin-ning in 1736 when EULER considered the (gen-eral case of the)K nigsberg bridge problem:Does there exist a walk crossing each of theseven bridges of K nigsberg exactly once? (So-lutio Problematis ad geometriam situs perti-nentis,Commentarii Academiae Scientiarum Impe-rialis Petropolitanae8 (1736), pp.)

R.J. WILSON, “Introduction to Graph Theory”, Longman, (3rd ed.) 1985. In theselectures we study combinatorial aspects of graphs.For more algebraic topics and methods,see

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