Equitable colorings of hypergraphs with few edges
Equitable colorings of hypergraphs with few edges
复制标题
少边超图的公平着色
DOI：
10.1016/j.dam.2019.03.024
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
D. Shabanov
中科院分区：
文献类型：
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作者：
M. Akhmejanova;D. Shabanov
研究了一致超图的公平染色的一个极值问题。回想一下，超图H的顶点着色如果在该着色下没有单色边，则称为固有着色。如果有r种颜色的适当着色，使得任意两个颜色类的大小相差不超过一种，那么我们就说超图是公平可着色的。本文证明了边数| E (H)|≤0。1 n n n n r−1 r r n−1，则当r< lnn 5时，超图H是完全可色的。
The paper deals with an extremal problem concerning equitable colorings of uniform hypergraph. Recall that a vertex coloring of a hypergraph H is called proper if there are no monochromatic edges under this coloring. A hypergraph is said to be equitably r-colorable if there is a proper coloring with r colors such that the sizes of any two color classes differ by at most one. In the present paper we prove that if the number of edges| E (H)|≤ 0. 01 n ln n r− 1 r r n− 1 then the hypergraph H is equitably r-colorable provided r< ln n 5.