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具有最小连通点对图的C-超图的染色讨论

刁科凤,赵 平   

  1. 临沂师范学院数学系, 山东临沂276005
  • 收稿日期:2006-03-10 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
  • 通讯作者: 刁科凤

On the coloring of C-hypergraphs with minimum connected pair graphs

DIAO Ke-feng and ZHAO Ping   

  1. Department of Mathematics, Linyi Normal University, Linyi 276005, Shandong, China
  • Received:2006-03-10 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
  • Contact: DIAO Ke-feng

摘要: 主要讨论C-超图的染色与点的点对图的连通性之间的关系,证明了对任意给定的不小于3的正整数n,都存在上色数为n且具有最小连通点对图的3一致C-超图.

关键词: 混合超图, 严格染色, 点对图 , 上色数

Abstract: The upper (lower) chromatic number X(H) of a mixed hypergraph H=(A,B,C) is the maximum (minimum) number of colors that can be assigned to the vertices of H in such a way that each C-edgecontains a monochromatic pair of vertices and each D-edge has two vertices colored differently. The upper (lower) chromatic number of a mixed hypergraph is colosely related to the number of edges, and the number of edges is colosely related to the connectness of the pair graphs of its vertices. In this paper we diascuss the relationship between the coloring and the connectess of the pair graphs of its vertices of a C-hypergraph, and we prove that for any positive integer n(≥3), there exists a 3-uniform C-hypergraph with upper chromatic number n and minimum connectedpair graphs.

Key words: pair graph , upper chromatic number, strict coloring, mixed hypergraph

中图分类号: 

  • O157.5
[1] 刘洪平 赵平 许娟. 一类弱惟一染色B-超图的构造及其最小点数[J]. J4, 2010, 45(2): 5-9.
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