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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
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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) · JFM 44.0568.01
[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) · JFM 63.0552.01
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