Graphs on Surfaces
Bojan Mohar and Carsten Thomassen
Johns Hopkins University Press
![](Book/JHUBookCover.gif)
The book Graphs on Surfaces has appeared in July 2001, published by
the Johns Hopkins University Press.
The book can be ordered online:
Some open problems from the book and
progres towards their solution.
Errata
Table of contents
Preface
Chapter 1   Introduction
1.1   Basic definitions
1.2   Trees and bipartite graphs
1.3   Blocks
1.4   ConnectivityChapter 2  
Planar graphs
2.1   Planar graphs and the Jordan Curve Theorem
2.2   The Jordan-Schonflies Theorem
2.3   The Theorem of Kuratowski
2.4   Characterizations of planar graphs
2.5   3-connected planar graphs
2.6   Dual graphs
2.7   Planarity algorithms
2.8   Circle packing representations
2.9   The Riemann Mapping Theorem
2.10   The Jordan Curve Theorem and Kuratowski's Theorem in general topological spacesChapter 3  
Surfaces
3.1   Classification of surfaces
3.2   Rotation systems
3.3   Embedding schemes
3.4   The genus of a graph
3.5   Classification of noncompact surfacesChapter 4  
Embeddings combinatorially, contractibility of cycles, and the genus problem
4.1   Embeddings combinatorially
4.2   Cycles of embedded graphs
4.3   The 3-path-condition
4.4   The genus of a graph
4.5   The maximum genus of a graphChapter 5  
The width of embeddings
5.1   Edge-width
5.2   2-flippings and uniqueness of LEW-embeddings
5.3   Triangulations
5.4   Minimal triangulations of a given edge-width
5.5   Face-width
5.6   Minimal embeddings of a given face-width
5.7   Embeddings of planar graphs
5.8   The genus of a graph with a given orientable embedding
5.9   Face-width and surface minors
5.10   Face-width and embedding flexibility
5.11   Combinatorial properties of embedded graphs of large widthChapter 6  
Embedding extensions and obstructions
6.1   Forbidden subgraphs and forbidden minors
6.2   Bridges
6.3   Obstructions in a bridge
6.4   2-restricted embedding extensions
6.5   The forbidden subgraphs for the projective plane
6.6   The minimal forbidden subgraphs for general surfacesChapter 7  
Tree-width and the excluded minor theorem
7.1   Tree-width and the excluded grid theorem
7.2   Minimal obstructions of bounded tree-width
7.3   The excluded minor theorem for any fixed surfaceChapter 8  
Colorings of graphs on surfaces
8.1   Planar graphs are 5-colorable
8.2   The Four Color Theorem
8.3   Color critical graphs and the Heawood formula
8.4   Coloring in few colors
8.5   Graphs without short cyclesAppendix A
  The minimal forbidden subgraphs for the projective plane
Appendix B   The unavoidable configurations in planar triangulations
Bibliography
Revised:
januar 04, 2021.