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arXiv 1105.2672math.CO
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3-一致双超图的色谱

The chromatic spectrum of 3-uniform bi-hypergraphs

Ping Zhao, Kefeng Diao, Kaishun Wang

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摘要：

设$S=\{n_1,n_2,...,n_t\}$是一个有限的正整数集，其中有$\min(S)\geq 3$和$t\geq 2$。对任意正整数$s_1,s_2,...,s_t$，我们构造了一族具有可行集$S$和$r_{n_i}=s_i, i=1,2,...,t$的3-一致双超图${\cal H}$，其中每个$r_{n_i}$是${\cal H}$的色谱的第$n_i$个分量.因此，我们解决了Bujtás和Tuza在2008年提出的3-一致双超图的一个公开问题。此外，我们还找到了一族与自己的可行集和色谱相同的子超图。特别地，我们得到了3-一致双超图在任意可行集上的最小顶点数的一个小上界。

英文摘要：

Let $S=\{n_1,n_2,...,n_t\}$ be a finite set of positive integers with $\min(S)\geq 3$ and $t\geq 2$. For any positive integers $s_1,s_2,...,s_t$, we construct a family of 3-uniform bi-hypergraphs ${\cal H}$ with the feasible set $S$ and $r_{n_i}=s_i, i=1,2,...,t$, where each $r_{n_i}$ is the $n_i$th component of the chromatic spectrum of ${\cal H}$. As a result, we solve one open problem for 3-uniform bi-hypergraphs proposed by Bujtás and Tuza in 2008. Moreover, we find a family of sub-hypergraphs with the same feasible set and the same chromatic spectrum as it's own. In particular, we obtain a small upper bound on the minimum number of vertices in 3-uniform bi-hypergraphs with any given feasible set.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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