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目 录 Editor's Statement Foreword Introduction Chapter I Graphs and Subgraphs I.1 Definitions 1.2 Isomorphism 1.3 Subgraphs 1.4 Vertices of attachment 1.5 Components and connection 1.6 Deletion of an edge 1.7 Lists of nonisomorphic connected graphs 1.8 Bridges 1.9 Notes Exercises References Chapter II Contractions and the Theorem of Menger II.1 Contractions II.2 Contraction of an edge II.3 Vertices of attachment II.4 Separation numbers II.5 Menger's Theorem II.6 Hall's Theorem II.7 Notes Exercises References Chapter III 2-Connection III.1 Separable and 2-connected graphs III.2 Constructions for 2-connected graphs III.3 Blocks III.4 Arms III.5 Deletion and contraction of an edge II1.6 Notes Exercises References Chapter IV 3-Connection IV.1 Multiple connection IV.2 Some constructions for 3-connected graphs IV.3 3-blocks IV.4 Cleavages IV.5 Deletions and contractions of edges IV.6 The Wheel Theorem IV.7 Notes Exercises References Chapter V Reconstruction V.I The Reconstruction Problem V.2 Theory and practice V.3 Kelly's Lemma V.4 Edge-reconstruction V.5 Notes Exercises References Chapter VI Digraphs and Paths VI.1 Digraphs VI.2 Paths VI.3 The BEST Theorem VI.4 The Matrix-Tree Theorem VI.5 The Laws of Kirchhoff VI.6 Identification of vertices VI.7 Transportation Theory VI.8 Notes Exercises References Chapter VII Alternating Paths VII.1 Cursality VII.2 The bicursal subgraph VII.3 Bicursal units VII.4 Alternating barriers VII.5 f-factors and f-barriers VII.6 The f-factor theorem VII.7 Subgraphs of minimum deficiency VII.8 The bipartite case VII.9 A theorem of Erdos and Gallai VII.10 Notes Exercises References Chapter VIII Algebraic Duality VIII.I Chain-groups VIII.2 Primitive chains VIII.3 Regular chain-groups VIII.4 Cycles VIII.5 Coboundaries VIII.6 Reductions and contractions VIII.7 Algebraic duality VIII.8 Connectivity VIII.9 On transportation theory VIII.10 Incidence matrices VIII.11 Matroids VIII.12 Notes Exercises References Chapter IX Polynomials Associated with Graphs IX.1 V-functions IX.2 The chromatic polynomial IX.3 Colorings of graphs IX.4 The flow polynomial IX.5 Tait colorings IX.6 The dichromate of a graph IX.7 Some remarks on reconstruction IX.8 Notes Exercises References Chapter X Combinatorial Maps X.1 Definitions and preliminary theorems X.2 Orientability X.3 Duality X.4 Isomorphism X.5 Drawings of maps X.6 Angles X.7 Operations on maps X.8 Combinatorial surfaces X.9 Cycles and coboundaries X. 10 Notes Exercises References Chapter XI Planarity XI.1 Planar graphs XI.2 Spanning subgraphs XI.3 Jordan's Theorem XI.4 Connectivity in planar maps XI.5 The cross-cut Theorem XI.6 Bridges XI.7 An algorithm for planarity XI.8 Peripheral circuits in 3-connected graphs XI.9 Kuratowski's Theorem XI.10 Notes Exercises References Index

W.T.Tutte已故著名数学家，现代图论奠基人之一。他于1948年获得剑桥大学博士学位；1942年至1949年担任三一学院评论员；1948年至1962年执教于多伦多大学。他是加拿大皇家科学院院士，曾被授予Henry Marshall Tory奖。1982年，加拿大议会授予他Izaak Walton Killam纪念奖。创造本书外，他还著有拟阵论方面的书籍。他生前还多年担任《Journal of Combinatorial Theory》杂志主编。