András Gyárfás, Ryan R. Martin, Miklós Ruszinkó, Gábor N. Sárközy
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引用次数: 0
摘要
如果图的每个 4 循环都用四种不同的颜色着色,我们就称该图的适当边着色为 B 着色。让表示 B 染色所需的最小颜色数。 受早先关于 B 染色的论文的启发,我们在此考虑平面图和外平面图的最大度。我们证明,对于平面图、双方形平面图以及具有 .我们猜想,在足够大的情况下,对于平面图 , 和外平面图 .
Proper edge colorings of planar graphs with rainbow C4 ${C}_{4}$‐s
We call a proper edge coloring of a graph a B‐coloring if every 4‐cycle of is colored with four different colors. Let denote the smallest number of colors needed for a B‐coloring of . Motivated by earlier papers on B‐colorings, here we consider for planar and outerplanar graphs in terms of the maximum degree . We prove that for planar graphs, for bipartite planar graphs, and for outerplanar graphs with . We conjecture that, for sufficiently large, for planar , and for outerplanar .
期刊介绍:
The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences.
A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .