Allaire, Frank; Reiner Swart, Edward A systematic approach to the determination of reducible configurations in the four-color conjecture. (English) Zbl 0398.05034 J. Comb. Theory, Ser. B 25, 339-362 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 6 Documents MSC: 05C15 Coloring of graphs and hypergraphs 05-04 Software, source code, etc. for problems pertaining to combinatorics Keywords:Reducible Configurations; Minimal Planar Five Chromatic Graph PDF BibTeX XML Cite \textit{F. Allaire} and \textit{E. Reiner Swart}, J. Comb. Theory, Ser. B 25, 339--362 (1978; Zbl 0398.05034) Full Text: DOI References: [1] Bernhart, A., Six-rings in minimal five-color maps, Am. J. math., 69, 391-412, (1947) · Zbl 0033.40304 [2] Bernhart, F., Topics in graph theory related to the five color conjecture, () [3] Bernhart, F., Some remarks on open sets of colorings, () [4] Birkhoff, G.D., The reducibility of maps, Amer. J. math., 35, 114-128, (1913) [5] Birkhoff, G.D.; Lewis, D.C., Chromatic polynomials, Trans. amer. math. soc., 64, 355-451, (1946) · Zbl 0060.41601 [6] Cohen, D.I.A., Small rings in critical maps, Ph.D. thesis, (May, 1975), Harvard [7] Franklin, P., The four color problem, Amer. J. math., 44, 225-236, (1922) · JFM 48.0664.02 [8] Haken, W.R.G., On geographically good configurations, Notices amer. math. soc., 20, 704-A17, (1973) [9] Haken, W.R.G., An existence theorem for planar maps, J. combinatorial theory B, 14, 180-184, (1973) · Zbl 0259.05103 [10] Heesch, H., () [11] Kurosh, A.G., () [12] Vaidyanathaswamy, R., () [13] Whitney, H.; Tutte, W.T., Kempe chains and the four colour problem, Utilitas math., 2, 241-281, (1972) · Zbl 0253.05120 [14] Winn, C.E., A case of coloration in the four color problem, Amer. J. math., 59, 515-529, (1937) · Zbl 0017.13203 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.