无$(P_7,C_4,C_5)$图的最优$χ$界
The optimal $χ$-bound for $(P_7,C_4,C_5)$-free graphs
摘要：
本文给出了一类无$(P_7,C_4,C_5)$图的最优$(P_7,C_4,C_5)$-结合函数.我们证明了每个无$(P_7,C_4,C_5)$图$G$都有$χ(G)\le \lceil \frac{11}{9}ω(G) \rceil$ .为了证明这个结果，我们使用[K. Cameron和S.我和黄。Penev和V. Sivaraman，无$({P}_7,{C}_4,{C}_5)$图的类：分解、算法和$χ$ -有界性，图论杂志93，503- 552，2020]结合了仔细的归纳论证和柯尼希定理在二分匹配中的非平凡应用。
英文摘要：
In this paper, we give an optimal $χ$-binding function for the class of $(P_7,C_4,C_5)$-free graphs. We show that every $(P_7,C_4,C_5)$-free graph $G$ has $χ(G)\le \lceil \frac{11}{9}ω(G) \rceil$. To prove the result, we use a decomposition theorem obtained in [K. Cameron and S. Huang and I. Penev and V. Sivaraman, The class of $({P}_7,{C}_4,{C}_5)$-free graphs: Decomposition, algorithms, and $χ$-boundedness, Journal of Graph Theory 93, 503--552, 2020] combined with careful inductive arguments and a nontrivial use of the König theorem for bipartite matching.
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。
