An Erdős-Pósa theorem for induced packings of even cycles

Jungho Ahn; Lars Jaffke; O-joung Kwon; Paloma T. de Lima; Hyemi Park

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arXiv · 2610.22967

An Erdős-Pósa theorem for induced packings of even cycles

Jungho Ahn·Lars Jaffke·O-joung Kwon·Paloma T. de Lima·Hyemi Park

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Abstract

We show that for every graph $G$ and every positive integer $k$, $G$ contains either $k$ vertex-disjoint even cycles with no edges between distinct cycles, or a set of $O(k^2\log k)$ vertices whose closed neighborhood meets every even cycle of $G$. Moreover, we give a polynomial-time algorithm that outputs one of the two outcomes. As an application, we show that every $K_{1,t}$-free graph containing no induced packing of $k$ even cycles has tree-independence number $O(tk^2\log k)$, with a corresponding decomposition computable in polynomial time.

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BibTeX RIS

Jungho Ahn, Lars Jaffke, O-joung Kwon, Paloma T. de Lima, Hyemi Park. 2026-10-16. An Erdős-Pósa theorem for induced packings of even cycles. https://arxiv.org/abs/2610.22967

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