Bondy J.A., Murty U.S.R. Graph Theory with Applications

Издательство North-Holland, 1982, -271 pp.Graph theory is increasingly being used to model situations arising in the applied sciences. This text, in addition to treating the basic material in some depth, includes a wide variety of applications, both to real-world problems and to other branches of mathematics. Care has been taken to select applications which actually make use of theory, and do not merely employ the language of graphs. Among the topics included are connectivity, Euler tours and Hamilton cycles, matchings, coloring problems, planarity and network flows. Simple new proofs of theorems of Brooks, Chvatal, Tutte and Vizing are presented. Stress is laid, whenever possible, on constructive methods of proof, and several efficient algorithms are described. The many illustrations and exercises are complemented by a number of notable features, hints to harder exercises, a selection of interesting graphs with special properties, and a list of fifty unsolved problems. The text has developed from courses given by the authors at the University of Waterloo, Ontario, and is intended as an introduction to graph theory for senior mathematics undergraduates and graduates. It will also be of interest to students and workers in operations research, computer science and some branches of engineering.Graphs and SubgraphsTreesConnectivityEuler Tours and Hamilton CyclesMatchingsEdge ColouringsIndependent Sets and CliquesVertex ColouringsPlanar GraphsDirected GraphsNetworksThe Cycle Space and Bond SpaceI Hints to Starred ExercisesII Four Graphs and a Table of their PropertiesIII Some Interesting GraphsIV Unsolved ProblemsV Suggestions for Further Reading