On the Upper Chromatic Numbers of Mixed Interval Hypertrees
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- 作者：Ping Zhao ; Kefeng Diao
- 关键词：mixed hypergraph ; upper chromatic number ; mixed interval hypergraph ; mixed interval hypertree ; sieve number
- 刊名：Lecture Notes in Computer Science
- 出版时间：2007
- 出版年：2007
- 期刊代码：99_0302-9743
- 类别：cp
- 卷：4381
- 期：1
- 页码：272-277
- 数据来源：sp
摘要
A mixed hypergraph consists of a finite set and two families of subsets: C-edges and D-edges. In a coloring, every C-edge has at least two vertices of the same color, and every D-edge has at least two vertices colored differently. The maximum and minimum numbers of colors are called the lower and upper chromatic numbers, respectively. A mixed hypergraph H{\cal H} with vertex set X, C-edge set C{\cal C} and D-edge set D{\cal D} is usually denoted by H=(X, C, D){\cal H}=(X,\, {\cal C},\, {\cal D}) . E. Bulgaru and V. Voloshin proved that [`(c)](H)=|X|-s(H)\overline{\chi}({\cal H})=|X|-s({\cal H}) holds for any mixed interval hypergraph ([3]), where s(H)s({\cal H}) is the sieve number of H{\cal H} . In this paper we prove that [`(c)](H)=|X|-s(H)\overline{\chi}({\cal H})=|X|-s({\cal H}) also holds for any mixed interval hypertree.