D. Archdeacon, J. Hutchinson, A. Nakamoto, S. Negami, and K. Ota, Chromatic numbers of quadrangulations of closed surfaces, preprint. Home/Search Document Details and Download
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Coloring Locally Bipartite Graphs on Surfaces - Mohar, Seymour (2000) (1 citation) (Correct)
....cycle. If G is as in the proof of Theorem 4.1, then any cycle passing through all g Mobius strips bounded by C 1 , C g is orientizing. This yields another formulation of Theorem 4. 1(c) whose only if part was discovered independently by Archdeacon, Hutchinson, Nakamoto, Negami, and Ota [1]. Corollary 4.2 If G is a quadrangulation of N g and the edge width of G is su#ciently large, then there is an orientizing cycle C, and G is 3 colorable if and only if C is of even length. ....
D. Archdeacon, J. Hutchinson, A. Nakamoto, S. Negami, and K. Ota, Chromatic numbers of quadrangulations of closed surfaces, preprint.
Extending Colorings of Locally Planar Graphs - Albertson, Hutchinson (1999) Self-citation (Hutchinson) (Correct)
....with arbitrarily large width [35] Starring each face in these 4 chromatic examples gives 5 chromatic graphs. This shows that Theorem 4 does not carry over to nonorientable surfaces. Properties of large width 4 chromatic quadrangulations and 5 chromatic Eulerian triangulations have been studied in [9]. Question 2 Does a large width projective planar graph, not containing a nonbipartite quadrangulation, have a 3 color extension theorem We include an argument of Gimbel and Thomassen showing that projective planar graphs without contractible 3 cycles do satisfy a 4 color extension theorem. ....
Dan Archdeacon, Joan Hutchinson, Atsuhiro Nakamoto, Seiya Negami, and Katsuhiro Ota, Chromatic numbers of quadrangulations of closed surfaces, submitted. 13
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