文章基本信息

标题：Chromatic Spectrum of K s -WORM Colorings of K n *
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作者：Julian A.D. Allagan ; Kenneth L. Jones
期刊名称：Computer Science Journal of Moldova
印刷版ISSN：1561-4042
出版年度：2020
卷号：28
期号：2
页码：170-186
出版社：Institute of Mathematics and Computer Science
摘要：An {\it $H$-WORM} coloring of a simple graph $G$ is the coloring of the vertices of $G$ such that no copy of $H\subseteq G$ is monochrome or rainbow. In a recently published article by one of the authors \cite{All1}, it was claimed that the number of $r$-partitions in a $K_s$-WORM coloring of $K_n$ is $ \zeta_r=\stirr{n}{r}$, where $\stirr{n}{r}$ denotes the Stirling number of the second kind, for all $3\le r\le s < n$. We found that $ \displaystyle \zeta_r = \stirr{n}{r}$ if and only if ${\lceil \frac{n+3}{2} \rceil}
关键词：Catalan numbers; Chromatic spectrum; Mixed hypergraph coloring; Stirling numbers.