On the Erdős-Pósa property for long holes in C_4-free graphs
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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 ∈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 [Erdős-Pósa property of chordless cycles and its applications. JCTB 2020].
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