J4 ›› 2011, Vol. 46 ›› Issue (2): 42-44.
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孙磊,马迎雪
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国家自然科学基金资助项目(60673047)；山东省高等学校科技计划项目(J10LA11)
SUN Lei, MA Ying-xue
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摘要：
给定正整数r, 图G的一个r-条件染色是G的顶点的一个正常染色，使得G中任意度数为d(v) 的顶点v, 其邻域中至少出现min｛r, d(v)｝ 种不同的颜色。若图的r-条件色数等于色数, 则称图为r-正常的。给出了判断一个图G为正常图的一些充分条件,并用实例说明了这些条件并非必要的。
关键词: 条件染色;条件色数;正常图
Abstract:
For positive integer r, a r-conditional coloring of a graph G is a proper vertex coloring of G such that every vertex v of degree d(v) in G is adjacent to vertices with at least min｛r, d(v)｝ different colors. A graph G is r-normal, if the r-conditional chromatic number of G equals the chromatic number of G. The conditions, which are sufficient for a graph to be normal, are given. Some examples are given to illustrate the conditions are not necessary.
Key words: conditional coloring; conditional chromatic number; normal graph
孙磊,马迎雪. 条件染色正常图的几个充分条件[J]. J4, 2011, 46(2): 42-44.
SUN Lei, MA Ying-xue. Several sufficient conditions of a normal graph in conditional coloring[J]. J4, 2011, 46(2): 42-44.
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http://lxbwk.njournal.sdu.edu.cn/CN/Y2011/V46/I2/42
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