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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