Acta mathematica scientia,Series B ›› 2001, Vol. 21 ›› Issue (2): 243-248.
• Articles • Previous Articles Next Articles
WANG Wei-Fan, ZHANG Ke-Min
Online:
Published:
Abstract:
Melnikov(1975) conjectured that the edges and faces of a plane graph G can be colored with (G) + 3 colors so that any two adjacent or incident elements receive distinct colors, where (G) denotes the maximum degree of G. This paper proves the conjecture for the case (G) 4.
Key words: Plane graph, chromatic number, coloring
CLC Number:
WANG Wei-Fan, ZHANG Ke-Min. A SEVEN-COLOR THEOREM ON EDGE-FACE COLORING OF PLANE GRAPHS[J].Acta mathematica scientia,Series B, 2001, 21(2): 243-248.
0 / / Recommend
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
URL: http://121.43.60.238/sxwlxbB/EN/
http://121.43.60.238/sxwlxbB/EN/Y2001/V21/I2/243
[1]Bondy J A, Murty U S R. Graph Theory with Applications. New York: Macmillan Press, 1976 [2]Borodin O V. Simultaneous coloring of edges and faces of plane graphs. Discrete Math, 1994, 128: 2133 [3]Lin Cuiqin, Hu Guanzhang, Zhang Zhongfu. A six-color theorem for the edge-face coloring of plane graphs.Discrete Math, 1995, 141: 291297. [4]Melnikov L S. Recent advances in graph theory. In: Fiedler M ed. Proc. Symposium. Prague: Academic Press, 1975. 543 [5]Wang Weifan. The edge-face chromatic number of plane graphs with lower degree. Applied Math-A J Chinese Universities Ser A, 1993, 8(3): 300307
Cited