Pearls in Graph Theory : A Comprehensive Introduction
Covers elementary concepts, major topics and theorems in graph theory, with an exposition of some more advanced topics. This edition includes two dozen new exercises, an augmented section on labelling and the simplification of many proofs.
- Hardback | 246 pages
- 157.48 x 231.14 x 22.86mm | 703.06g
- 01 Aug 1994
- Elsevier Science Publishing Co Inc
- Academic Press Inc
- San Diego, United States
- 2nd Revised edition
- references, index
Table of contents
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.