×

Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces. (English) Zbl 1075.05532

Alavi, Yousef (ed.) et al., Papers of the 9th quadrennial international conference on graph theory, combinatorics, algorithms, and applications, Kalamazoo, MI, USA, June 4–9, 2000. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 11, 509-518 (2002).
For the entire collection see [Zbl 1074.05003].

MSC:

05C15 Coloring of graphs and hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
PDFBibTeX XMLCite
Full Text: Link

References:

[1] Archdeacon, D.; Hutchinson, J. P.; Nakamoto, A.; Negami, S.; Ota, K.: Chromatic numbers of quadrangulations on closed surfaces. J. graph theory 37, 100-114 (2001) · Zbl 0979.05034
[2] Fisk, S.; Mohar, B.: Coloring graphs without short non-bounding cycles. J. combin. Theory, ser. B 60, 268-276 (1994) · Zbl 0793.05058
[3] Gimbel, J.; Thomassen, C.: Coloring graphs with fixed genus and girth. Trans. AMS, No. No. 11, 4555-4564 (1997) · Zbl 0884.05039
[4] N, Hartsfield, The quadrangular genus of complete graphs, preprint. · Zbl 0836.05019
[5] Hutchinson, J. P.: Three-coloring graphs embedded on surfaces with all faces even-sided. J. combin. Theory ser. B 65, 139-155 (1995) · Zbl 0828.05029
[6] J.P. Hutchinson, On coloring maps made from Eulerian graphs, ”Proceeding of 5th British Combinatorial Conference, 1975”, 343–354.
[7] Mohar B. and Seymour P. D., Coloring locally bipartite graphs on surfaces, preprint. · Zbl 1079.05027
[8] Nakamoto, A.: Diagonal transformations in quadrangulations of surfaces. J. graph theory 21, 289-299 (1996) · Zbl 0854.05038
[9] Nakamoto, A.: Diagonal transformations and cycle parities of quadrangulations on surfaces. J. combin. Theory, ser. B 67, 202-211 (1996) · Zbl 0857.05024
[10] Nakamoto, A.; Ota, K.: Diagonal transformations in quadrangulations and Dehn twists preserving cycle parties. J. combin. Theory, ser. B 69, 125-141 (1997) · Zbl 0874.05021
[11] Nakamoto, A.; Ota, K.: Diagonal transformations of graphs and Dehn twists of surfaces. J. combin. Theory ser. B 70, 292-300 (1997) · Zbl 0873.05040
[12] Negami, S.; Nakamoto, A.: Diagonal transformations of graphs on closed surfaces. Sci. rep. Yokohama nat. Univ., sec. I 40, 71-97 (1993)
[13] Robertson, N.; Seymour, P.: Graph minors. VII disjoint paths on a surface. J. combin. Theory, ser. B 45, 212-254 (1988) · Zbl 0658.05044
[14] Robertson, N.; Vitray, R.: Representativity of surface embeddings. ”Paths, flows, and VLSI-layout” (Bonn, 1988), 293–328, algorithms combin 9 (1990) · Zbl 0735.05032
[15] Youngs, D. A.: 4-chromatic projective graphs. J. graph theory 21, 219-227 (1996) · Zbl 0839.05040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.