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Appel, K.; Haken, W.

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

J. Comb. Theory, Ser. B 26, 1-21 (1979).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0407.05035

Cited in 2 Documents

MSC:

05C15 Coloring of graphs and hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory

Keywords:

Four Color Problem; Unavoidable Set of Configurations; Planar Triangulations

Citations:

Zbl 0387.05009; Zbl 0344.05013; Zbl 0387.05010
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\textit{K. Appel} and \textit{W. Haken}, J. Comb. Theory, Ser. B 26, 1--21 (1979; Zbl 0407.05035)
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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] {\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
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.