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Abstract: this paper we focus on the torus and on ostensibly the most dicult case when the graph is a six-regular triangulation; in [28] Thomassen asks for a characterization of the non-4-colorable, 6-regular graphs on the torus. A theorem of Altshuler [4] shows that every 6regular toroidal graph can be represented as a 6-regular shifted rectangular grid on the torus; see Figure 2. A shift of one is the same as an unshifted grid. This allows us to focus rst on 6-regular grids and then to extend our... (Update)
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BibTeX entry: (Update)
Karen L. Collins and Joan P. Hutchinson, Four-coloring six-regular graphs on the torus, Centre de Recherches Mathe'matiques, CRM Proceedings and Lecture Notes, Vol. 23, 1999, 21-34. http://citeseer.ist.psu.edu/collins99fourcoloring.html More
@misc{ collins99fourcoloring,
author = "K. Collins and J. Hutchinson",
title = "Four-coloring six-regular graphs on the torus",
text = "Karen L. Collins and Joan P. Hutchinson, Four-coloring six-regular graphs
on the torus, Centre de Recherches Mathe'matiques, CRM Proceedings and Lecture
Notes, Vol. 23, 1999, 21-34.",
year = "1999",
url = "citeseer.ist.psu.edu/collins99fourcoloring.html" }
Citations (may not include all citations):168 Introduction to Graph Theory (context) - West - 1996
153 Graph Coloring Problems (context) - Jensen, Toft - 1995
151 Every planar map is four colorable (context) - Appel, Haken - 1976
39 The four colour theorem (context) - Robertson, Sanders et al. - 1997
22 Map Color Theorem (context) - Ringel - 1974
19 Computers and Intractibility (context) - Garey, Johnson - 1979
18 Map-colour theorem (context) - Heawood
14 Solution of the Heawood map-coloring problem (context) - Ringel, Youngs - 1968
9 the geographical problem of the four colours (context) - Kempe
7 The state of the three color problem (context) - Steinberg - 1993
7 chromatic projective graphs (context) - Youngs - 1996
7 Construction and enumeration of regular maps on the torus (context) - Altshuler - 1973
7 Embeddings of graphs with no short noncontractible cycles (context) - Thomassen - 1990
4 An update on the state of the three color problem (context) - Steinberg - 1993
4 Three-coloring graphs embedded on surfaces with all faces ev.. (context) - Hutchinson - 1995
[Article contains additional citations not shown here]
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