A Textbook of Graph Theory (Universitext) - Hardcover

Balakrishnan, R.; Ranganathan, K.

Hardcover

ISBN 10: 0387988599 ISBN 13: 9780387988597

Verlag: Springer, 1999

Inhaltsangabe

I Basic Results.- 1.0 Introduction.- 1.1 Basic Concepts.- 1.2 Subgraphs.- 1.3 Degrees of Vertices.- 1.4 Paths and Connectedness.- 1.5 Automorphism of a Simple Graph.- 1.6 Line Graphs.- 1.7 Operations on Graphs.- 1.8 An Application to Chemistry.- 1.9 Miscellaneous Exercises.- Notes.- II Directed Graphs.- 2.0 Introduction.- 2.1 Basic Concepts.- 2.2 Tournaments.- 2.3 K-Partite Tournaments.- Notes.- III Connectivity.- 3.0 Introduction.- 3.1 Vertex Cuts and Edge Cuts.- 3.2 Connectivity and Edge-Connectivity.- 3.3 Blocks.- 3.4 Edge-Connectivity of a Graph.- 3.5 Menger's Theorem.- 3.6 Exercises.- Notes.- IV Trees.- 4.0 Introduction.- 4.1 Definition, Characterization, and Simple Properties.- 4.2 Centers and Centroids.- 4.3 Counting the Number of Spanning Trees.- 4.4 4.4 Cayley's Formula.- 4.5 Helly Property.- 4.6 Exercises.- Notes.- V Independent Sets and Matchings.- 5.0 Introduction.- 5.1 Vertex Independent Sets and Vertex Coverings.- 5.2 Edge-Independent Sets.- 5.3 Matchings and Factors.- 5.4 Matchings in Bipartite Graphs.- 5.5 * Perfect Matchings and the Tutte Matrix.- Notes.- VI Eulerian and Hamiltonian Graphs.- 6.0 Introduction.- 6.1 Eulerian Graphs.- 6.2 Hamiltonian Graphs.- 6.3 * Pancyclic Graphs.- 6.4 Hamilton Cycles in Line Graphs.- 6.5 2-Factorable Graphs.- 6.6 Exercises.- Notes.- VII Graph Colorings.- 7.0 Introduction.- 7.1 Vertex Colorings.- 7.2 Critical Graphs.- 7.3 Triangle-Free Graphs.- 7.4 Edge Colorings of Graphs.- 7.5 Snarks.- 7.6 Kirkman's Schoolgirls Problem.- 7.7 Chromatic Polynomials.- Notes.- VIII Planarity.- 8.0 Introduction.- 8.1 Planar and Nonplanar Graphs.- 8.2 Euler Formula and Its Consequences.- 8.3 K5 and K3,3 are Nonplanar Graphs.- 8.4 Dual of a Plane Graph.- 8.5 The Four-Color Theorem and the Heawood Five-Color Theorem.- 8.6 Kuratowski's Theorem.- 8.7 Hamiltonian Plane Graphs.- 8.8 Tait Coloring.- Notes.- IX Triangulated Graphs.- 9.0 Introduction.- 9.1 Perfect Graphs.- 9.2 Triangulated Graphs.- 9.3 Interval Graphs.- 9.4 Bipartite Graph B(G)of a Graph G.- 9.5 Circular Arc Graphs.- 9.6 Exercises.- 9.7 Phasing of Traffic Lights at a Road Junction.- Notes.- X Applications.- 10.0 Introduction.- 10.1 The Connector Problem.- 10.2 Kruskal's Algorithm.- 10.3 Prim's Algorithm.- 10.4 Shortest-Path Problems.- 10.5 Timetable Problem.- 10.6 Application to Social Psychology.- 10.7 Exercises.- Notes.- List of Symbols.- References.

Über diesen Titel

Reseña del editor

Here is a solid introduction to graph theory, covering Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, Fournier's proof of Kuratowski's theorem on planar graphs, and more. The book does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1999
• Sprache: Englisch
• ISBN 10: 0387988599
• ISBN 13: 9780387988597
• Einband: Tapa dura
• Anzahl der Seiten: 244
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland