×

An unavoidable set of configurations in planar trigangulations. (English) Zbl 0407.05035


MSC:

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

References:

[1] Allaire, F.; Swart, E. R., A systematic approach to the determination of reducible configurations in the four-colour conjecture, J. Combinatorial Theory B, 25, 339-362 (1978) · Zbl 0398.05034
[2] Appel, K.; Haken, W., The existence of unavoidable sets of geographically good configurations, Illinois J. Math., 20, 218-297 (1976) · Zbl 0322.05141
[3] Bernhart, A., Another reducible edge configuration, Amer. J. Math., 70, 144-146 (1948) · Zbl 0034.40102
[4] F. BernhartJ. Combinatorial Theory B; F. BernhartJ. Combinatorial Theory B · Zbl 0097.37101
[5] Birkhoff, G. D., The reducibility of maps, Amer. J. Math., 35, 114-128 (1913)
[6] Haken, W., An existence theorem for planar maps, J. Combinatorial theory B, 14, 180-184 (1973) · Zbl 0259.05103
[7] Heesch, H., (Untersuchungen zum Vierfargenproblem, B-I-Hochschulskripten 810/810a/810b (1969), Bibliographisches Institut: Bibliographisches Institut Mannheim/Vienna/Zurich)
[8] Heesch, H., Chromatic reduction of the triangulations \(T_e, e = e_5 + e_7\), J. Combinatorial Theory B, 13, 46-55 (1972) · Zbl 0242.05110
[9] Ore, O., (The Four-Color Problem (1967), Academic Press: Academic Press New York/London) · Zbl 0149.21101
[10] Stromquist, W., Some Aspects of the Four Color Problem, (Ph.D. Thesis (1975), Harvard University)
[11] Tutte, W.; Whitney, H., Kempe chains and the four colour problem, Utilitas Mathematica, 2, 241-281 (1972) · Zbl 0253.05120
[12] Winn, C., A case of coloration in the four color problem, Amer. J. Math., 59, 515-528 (1937)
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.