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

05C15 Coloring of graphs and hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
Full Text: DOI
[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] \scF. Bernhart, On the characterization of reductions of small order, J. Combinatorial Theory B, to appear. · 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, ()
[8] Heesch, H, Chromatic reduction of the triangulations Te, e = e5 + e7, J. combinatorial theory B, 13, 46-55, (1972) · Zbl 0242.05110
[9] Ore, O, ()
[10] Stromquist, W, Some aspects of the four color problem, ()
[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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