Pearls in Graph Theory

Part 1 Basic graph theory: graphs and degrees of vertices; subgraphs, isomorphic graphs, trees. Part 2 Colourings of graphs: vertex colourings; edge colourings; decompositions and Hamilton cycles; more decompositions. Part 3 Circuits and cycles: Eulerian circuits; the Oberwolfach Problem; infinite lattice graphs. Part 4 Extremal problems: a theorem of Turan; cages; Ramsey theory. Part 5 Counting: counting 1-factors; Cayley's Spanning Tree formula; more spanning trees. Part 6 Labelling graphs: magic graphs and graceful trees; conservative graphs. Part 7 Applications and algorithms: spanning tree algorithms; matchings in graphs, scheduling problems; binary trees and prefix codes. Part 7 Drawings of graphs: planar graphs; the four colour theorem; the five colour theorem; graphs and geometry. Part 8 Measurements of closeness to planarity: crossing number; thickness and splitting number; Heawood's Empire Problem. Part 9 Graphs on surfaces: rotations of graphs; planar graphs revisited; the genus of a graph.