On the Erd\H{o}s-P\'osa property for long holes in $C_4$-free graphs

We prove that there exists a function $f (k) = O (k^{2} \log k)$ such that for every $C_{4}$ -free graph $G$ and every $k \in N$ , $G$ either contains $k$ vertex-disjoint holes of length at least $6$ , or a set $X$ of at most $f (k)$ vertices such that $G - X$ has no hole of length at least $6$ . This answers a question of Kim and Kwon [Erd\H{o}s-P'osa property of chordless cycles and its applications. JCTB 2020].

On the Erd\H{o}s-P\'osa property for long holes in $C_{4}$ -free graphs

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On the Erd\H{o}s-P\'osa property for long holes in $C_{4}$ -free graphs

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On the Erd\H{o}s-P\'osa property for long holes in C4C4​-free graphs

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On the Erd\H{o}s-P\'osa property for long holes in C4C4​-free graphs

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On the Erd\H{o}s-P\'osa property for long holes in $C_{4}$ -free graphs

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On the Erd\H{o}s-P\'osa property for long holes in $C_{4}$ -free graphs

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AI智能校验