arXiv 1903.094032019-03-22math.CO

无K_{1,3}完美图的禁止诱导子图

On forbidden induced subgraphs for K_{1,3}-free perfect graphs

Christoph Brause, Přemysl Holub, Adam Kabela, Zdeněk Ryjáček, Ingo Schiermeyer, Petr Vrána

摘要：

考虑独立数至少为$3$的连通无$K_{1,3}$图，Chudnovsky和Seymour（2010）证明了每个这样的图，比如$G$，是$2ω$ -簇，其中$ω$表示$G$的团数。我们研究了无$(K_{1,3}, Y)$图，证明了以下三个命题是等价的。(1)每一个与奇圈不同且独立数至少为$3$的连通无$(K_{1,3}, Y)$图都是完美图. (2)每一个与奇圈不同且独立数至少为$3$的连通无$(K_{1,3}, Y)$图都是$ω$ -列图. (3)$Y$同构于$P_5$或$Z_2$的导出子图（其中$Z_2$也称为hammer）。此外，对于连接的$(K_{1,3}, Y)$ -自由图（没有独立数的假设），我们显示了一个类似的特征图$P_4$和$Z_1$（其中$Z_1$也被称为爪）。

英文摘要：

Considering connected $K_{1,3}$-free graphs with independence number at least $3$, Chudnovsky and Seymour (2010) showed that every such graph, say $G$, is $2ω$-colourable where $ω$ denotes the clique number of $G$. We study $(K_{1,3}, Y)$-free graphs, and show that the following three statements are equivalent. (1) Every connected $(K_{1,3}, Y)$-free graph which is distinct from an odd cycle and which has independence number at least $3$ is perfect. (2) Every connected $(K_{1,3}, Y)$-free graph which is distinct from an odd cycle and which has independence number at least $3$ is $ω$-colourable. (3) $Y$ is isomorphic to an induced subgraph of $P_5$ or $Z_2$ (where $Z_2$ is also known as hammer). Furthermore, for connected $(K_{1,3}, Y)$-free graphs (without an assumption on the independence number), we show a similar characterisation featuring the graphs $P_4$ and $Z_1$ (where $Z_1$ is also known as paw).

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。

摘要：

英文摘要：

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