The theory of graphs : and its applications / by Claude Berge ; translated by Alison Doig.
Idioma: Inglés Lenguaje original: Francés Editor: London : New York : Methuen ; John Wiley & Sons, 1962Descripción: x, 247 p. ; 23 cmTítulos uniformes: Théorie des graphes et ses applications. Inglés Otra clasificación: 05Cxx1 General Definitions Sets and Multivalued Functions [1] Paths and Circuits of a Graph [5] Chains and Cycles of a Graph [8] 2 Descendance Relations Weak Ordering Associated with a Graph [11] Inductive Graphs and Bases [13] 3 The Ordinal Function and the Grundy Function on an Infinite Graph General Remarks Concerning Infinite Graphs [16] Ordinal Function [19] Grundy Functions [22] Operations over Graphs [23] 4 The Fundamental Numbers of the Theory of Graphs Cyclomatic Number [27] Chromatic Number [30] Methods for Finding the Chromatic Number [33] Coefficient of Internal Stability [35] Coefficient of External Stability [40] 5 Kernels of a Graph Existence and Uniqueness Theorems [45] Application to Grundy Functions [50] 6 Games on a Graph Nim Type Games [52] The General Definition of a Game (with Perfect Information) [58] Strategies [60] 7 The Problem of the Shortest Route Stepwise Procedures [65] Various Generalizations [68] 8 Transport Networks The Problem of Maximum Flow [71] The Problem of Minimum Flow [77] Problems of Flow when a Set of Values is Associated with each Arc [77] Infinite Transport Networks [84] 9 The Theorem of the Demi-Degrees Inward or Outward Demi-Degree [86] 10 Matching of a Simple Graph The Maximum Matching Problem [92] Deficiency of a Simple Graph [96] The Hungarian Method [99] Extensions to the Infinite Case [102] Application to the Theory of Matrices [105] 11 Factors Hamiltonian Paths and Circuits [107] Factors and Methods for Determining Them [111] The Problem of Finding a Partial Graph with Given Demi-Degrees [117] 12 Centres of a Graph Centres [119] Radius [120] 13 The Diameter of a Strongly Connected Graph General Remarks on Strongly Connected Graphs without Loops [123] Diameter [126] 14 The Matrix Associated with a Graph The Use of Standard Matrix Operations [130] Problems of Enumeration [132] The Problem of the Leader [135] The Use of Boolean Operations [138] 15 Incidence Matrices Matrices with the Unimodular Property [141] Systems with the Unimodular Property [146] Cyclomatic Matrices [149] 16 Trees and Arborescences Trees [152] Analytic Treatment [156] Arborescences [160] 17 Euler’s Problem Eulerian Cycles [165] Eulerian Circuits [167] 18 Matching in the General Case The Theory of Alternating Chains [171] The Determination of a Partial Graph with Given Degrees [174] Perfect Matching [178] Application to the Coefficient of Internal Stability [184] 19 Semi-Factors Hamiltonian Cycles and Semi-Factors [187] A Necessary and Sufficient Condition for the Existence of a Semi-Factor [192] 20 The Connectivity of a Graph Articulation Points [196] Biconnected Graphs [198] h-Connected Graphs [203] 21 Planar Graphs General Properties [207] Generalization [218] Appendix 1 Note on the General Theory of Games [220] Appendix 2 Note on Transport Problems [227] Bibliography [238] List of Symbols [245] Index of Terms Used [246]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 05 B495-2 (Browse shelf) | Available | A-1096 |
Traducción de: Théorie des graphes et ses applications. Paris : Dunod, 1958.
"This is the second book on graph theory ever written."--Math.Rev.
1 General Definitions --
Sets and Multivalued Functions [1] --
Paths and Circuits of a Graph [5] --
Chains and Cycles of a Graph [8] --
2 Descendance Relations --
Weak Ordering Associated with a Graph [11] --
Inductive Graphs and Bases [13] --
3 The Ordinal Function and the Grundy Function on an Infinite Graph --
General Remarks Concerning Infinite Graphs [16] --
Ordinal Function [19] --
Grundy Functions [22] --
Operations over Graphs [23] --
4 The Fundamental Numbers of the Theory of Graphs --
Cyclomatic Number [27] --
Chromatic Number [30] --
Methods for Finding the Chromatic Number [33] --
Coefficient of Internal Stability [35] --
Coefficient of External Stability [40] --
5 Kernels of a Graph --
Existence and Uniqueness Theorems [45] --
Application to Grundy Functions [50] --
6 Games on a Graph --
Nim Type Games [52] --
The General Definition of a Game (with Perfect Information) [58] --
Strategies [60] --
7 The Problem of the Shortest Route --
Stepwise Procedures [65] --
Various Generalizations [68] --
8 Transport Networks --
The Problem of Maximum Flow [71] --
The Problem of Minimum Flow [77] --
Problems of Flow when a Set of Values is Associated with each Arc [77] --
Infinite Transport Networks [84] --
9 The Theorem of the Demi-Degrees --
Inward or Outward Demi-Degree [86] --
10 Matching of a Simple Graph --
The Maximum Matching Problem [92] --
Deficiency of a Simple Graph [96] --
The Hungarian Method [99] --
Extensions to the Infinite Case [102] --
Application to the Theory of Matrices [105] --
11 Factors --
Hamiltonian Paths and Circuits [107] --
Factors and Methods for Determining Them [111] --
The Problem of Finding a Partial Graph with Given Demi-Degrees [117] --
12 Centres of a Graph --
Centres [119] --
Radius [120] --
13 The Diameter of a Strongly Connected Graph --
General Remarks on Strongly Connected Graphs without Loops [123] --
Diameter [126] --
14 The Matrix Associated with a Graph --
The Use of Standard Matrix Operations [130] --
Problems of Enumeration [132] --
The Problem of the Leader [135] --
The Use of Boolean Operations [138] --
15 Incidence Matrices --
Matrices with the Unimodular Property [141] --
Systems with the Unimodular Property [146] --
Cyclomatic Matrices [149] --
16 Trees and Arborescences --
Trees [152] --
Analytic Treatment [156] --
Arborescences [160] --
17 Euler’s Problem --
Eulerian Cycles [165] --
Eulerian Circuits [167] --
18 Matching in the General Case --
The Theory of Alternating Chains [171] --
The Determination of a Partial Graph with Given Degrees [174] --
Perfect Matching [178] --
Application to the Coefficient of Internal Stability [184] --
19 Semi-Factors --
Hamiltonian Cycles and Semi-Factors [187] --
A Necessary and Sufficient Condition for the Existence of a Semi-Factor [192] --
20 The Connectivity of a Graph --
Articulation Points [196] --
Biconnected Graphs [198] --
h-Connected Graphs [203] --
21 Planar Graphs --
General Properties [207] --
Generalization [218] --
Appendix 1 Note on the General Theory of Games [220] --
Appendix 2 Note on Transport Problems [227] --
Bibliography [238] --
List of Symbols [245] --
Index of Terms Used [246] --
MR, 24 #A2381
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