| 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 |
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