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- W4311409813 abstract "In this paper, we give an optimal $chi$-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 $chi(G)le lceil frac{11}{9}omega(G) rceil$. 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 $chi$-boundedness, Journal of Graph Theory 93, 503--552, 2020] combined with careful inductive arguments and a nontrivial use of the K{o}nig theorem for bipartite matching." @default.
- W4311409813 created "2022-12-26" @default.
- W4311409813 creator A5073546070 @default.
- W4311409813 date "2022-12-10" @default.
- W4311409813 modified "2023-09-24" @default.
- W4311409813 title "The optimal $chi$-bound for $(P_7,C_4,C_5)$-free graphs" @default.
- W4311409813 doi "https://doi.org/10.48550/arxiv.2212.05239" @default.
- W4311409813 hasPublicationYear "2022" @default.
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