arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1608.07686math.CO
收藏

团覆盖与无爪图

Clique Coverings and Claw-free Graphs

Csilla Bujtás, Akbar Davoodi, Ervin Győri, Zsolt Tuza

备注：
12 pages
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

令$\cal C$是$E(G)$的团覆盖，令$v$是$G$的顶点。顶点$v$（相对于$\cal C$）的化合价，用$val_{\cal C}(v)$表示，是包含$v$的$\cal C$中的团的数目。定义$G$的局部团覆盖数$lcc(G)$为最小整数$k$，对于该最小整数，对每个顶点$v\in V(G)$，存在$E(G)$的团覆盖使得$val_{\cal C}(v)$至多为$k$.在本文中，除了其他结果，我们证明了，如果$G$是一个无爪图，那么$lcc(G)+χ(G)\leq n+1$。

英文摘要：

Let $\cal C$ be a clique covering for $E(G)$ and let $v$ be a vertex of $G$. The valency of vertex $v$ (with respect to $\cal C$), denoted by $val_{\cal C}(v)$, is the number of cliques in $\cal C$ containing $v$. The local clique cover number of $G$, denoted by $lcc(G)$, is defined as the smallest integer $k$, for which there exists a clique covering for $E(G)$ such that $val_{\cal C}(v)$ is at most $k$, for every vertex $v\in V(G)$. In this paper, among other results, we prove that if $G$ is a claw-free graph, then $lcc(G)+χ(G)\leq n+1$.

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。

↑