图的拓扑理论

本书不在于图的拓扑性质本身，而是着意以图为代表的一些组合构形为出发点，揭示与拓扑学中一些典型对??，如多面形、曲面、嵌入、纽结等的联系，特别是显示了定理有效化的途径对于以拓扑学为代表的基础数学的作用。同时，也提出了一些新的曲面模型，为超大规模集成电路的布线尝试构建多方面的理论基础。     本书可作为基础数学，应用数学、系统科学、计算机科学等专业高年级本科生和研究生的补充教材，也可供相关专业的教师和科研工作者参考。

Preface Chapter 1 Preliminaries   1.1 Sets and relations   1.2 Partitions and permutations   1.3 Graphs and networks   1.4 Groups and spaces   1.5 Notes Chapter 2 Polyhedra   2.1 Polygon double covers   2.2 Supports and skeletons   2.3 Orientable polyhedra   2.4 Nonorientable polyhedra   2.5 Classic polyhedra   2.6 Notes Chapter 3 Surfaces   3.1 Polyhegons   3.2 Surface closed curve axiom   3.3 Topological transformations   3.4 Complete invariants   3.5 Graphs on surfaces   3.6 Up-embeddability   3.7 Notes Chapter 4 Homology on Polyhedra   4.1 Double cover by travels   4.2 Homology   4.3 Cohomology   4.4 Bicycles   4.5 Notes Chapter 5 Polyhedra on the Sphere   5.1 Planar polyhedra   5.2 Jordan closed curve axiom   5.3 Uniqueness   5.4 Straight line representations   5.5 Convex representation   5.6 Notes Chapter 6 Automorphisms of a Polyhedron   6.1 Automorphisms   6.2 V-codes and F-codes   6.3 Determination of automorphisms   6.4 Asymmetrization   5.5 Notes Chapter 7 Gauss Crossing Sequences   7.1 Crossing polyhegons   7.2 Dehn‘s transformation   7.3 Algebraic principles   7.4 Gauss Crossing problem   7.5 Notes Chapter 8 Cohomology on Graphs   8.1 Immersions   8.2 Realization of planarity   8.3 Reductions   8.4 Planarity auxiliary graphs   8.5 Basic conclusions   8.6 Notes   …… Chapter 9  Embeddability on Surfaces Chapter 10 Embeddings on the Sphere Chapter 11 Orthogonality on Surfaces Chapter 12 Net Embeddings Chapter 13 Extremality on Surfaces Chapter 14 Matroial Graphicness Chapter 15 Knot Polynomials Bibliography Subject Index Author Index