曲面上色临界图点数的上界
Upper Bound for the Number of Vertices of Color-Critical Graphs on Surfaces
作者: 李青青 , 晁福刚 , 路伟华 , 任 韩 :华东师范大学数学系,上海;
关键词: 嵌入; 亏格; 着色; 色临界图; Embedding; Genus; Coloring; Color-Critical Graph
摘要:文章引用: 李青青 , 晁福刚 , 路伟华 , 任 韩 (2014) 曲面上色临界图点数的上界。 应用数学进展, 3, 49-53. doi: 10.12677/AAM.2014.32008
参考文献
[1] Möbius, A.F. (1861) Zur theorie der polyëder und elementarverwandtschaft. Qeuvres Complètes, 2, 519-559.
[2] Jordan, C. (1866) Sur la déormation des surfaces. Journal de Mathématiques Pures et Appliquées, 11, 105-109.
[3] Thomassen, C. (1992) The Jordan-Schönflies theorem and the classification of surfaces. The American Mathematical Monthly, 99, 116-130.
[4] Euler, L. (1752) Elementa doctrinae solidorum. Demonstratio nonnullarum insignium proprietatum. Novi Comment Acad. Sc. Imp. Petropol., 4, 109-160.
[5] Edmonds, J.R. (1960) A combinatorial representation for polyhedral surfaces. Notices of the AMS—American Mathematical Society, 7, 646.
[6] Heffter, L. (1891) Über das problem der nachbargebiete. Mathematische Annalen, 38, 477-508.
[7] Heawood, P.J. (1890) Map colour theorem. The Quarterly Journal of Pure and Applied Mathematics, 24, 332-338.
[8] Ringel, G. and Youngs, J.W.T. (1968) Solution of the Heawood map-coloring problem. Proceedings of the National Academy of Sciences of the USA, 60, 438-455.
[9] Franklin, P. (1934) A six color problem. Journal of Mathematical Physics, 13, 363-369.
[10] Dirac, G.A. (1952) Map color theorem. Canadian Journal of Mathematics, 4, 480-490.
[11] Albertson, M.O. and Hutchinson, J.P. (1977) The independence ratio and genus of a graph. Transactions of the American Mathematical Society, 226, 161-173.
[12] Gimbel, J. and Thomassen, C. (1997) Coloring graphs with fixed genus and girth. Transactions of the American Mathematical Society, 349, 4555-4564.
[13] Dirac, G.A. (1953) The coloring of maps. Journal of the London Mathematical Society, 28, 476-480.
[14] Mohar, B. and Thomassen, C. (2001) Graphs on surfaces. Johns Hopkins University Press, London.
[15] Gallai, T. (1963) Kritische graphen I, II. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 8, 165-192,373-395.
[16] Thomassen, C. (1994) Five-coloring graphs on the torus. Journal of Combinatorial Theory, Series B, 62, 11-33.
[17] Chenette, N., Postle, L., Streib, N. and Thomas, R. (2012) Five-colorings graphs on the Klein bottle. Journal of Combinatorial Theory, Series B, 102, 1067-1098.
[18] Kawarayabashi, K.I., Král, D., Kynčl, J. and Lidický, B. (2009) 6-critical graphs on the Klein bottle. SIAM Journal on Discrete Mathematics, 23, 372-383.