Extremal problems for panchromatic colourings of uniform hypergraphs
Extremal problems for panchromatic colourings of uniform hypergraphs
复制标题
均匀超图的全色着色极值问题
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. Shabanov
中科院分区：
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作者：
A. P. Rozovskaya;D. Shabanov
本文讨论了Kostochka提出的一个著名的超图极值理论问题。如果超图的每条边都包含所有颜色的顶点，那么将超图的顶点集着色为r种颜色的就是全色的。我们研究了特征p.n；R /等于没有全色R -着色的n-均匀超图的最小可能边数。我们找到了一个新的p。n的渐近下界；R /和一系列有关问题的结果。本研究由俄罗斯基础研究基金会资助（项目号：12-01 - 00683）、俄罗斯联邦总统支持主要科学院校计划资助（项目号：2519.2012.1）和俄罗斯联邦总统支持青年科学家计划资助（项目号：1122.2012.1）。
In this paper, we deal with the well-known problem of extremal theory of hypergraphs posed by A. V. Kostochka. A colouring of the set of vertices of a hypergraph into r colours is said to be a panchromatic one if each edge of the hypergraph contains vertices of all colours. We study the characteristic p.n; r/ equal to the minimum possible number of edges of an n-uniform hypergraph which has no panchromatic r-colourings. We find a new asymptotic lower bound for p.n; r/ and a series of results concerning related questions. This research was supported by the Russian Foundation for Basic Research, grant 12–01– 00683, by the Program of President of Russian Federation for support of leading scientific schools, grant 2519.2012.1, and by the Program of President of Russian Federation for support of young scientists, grant 1122.2012.1.