Long cycles have the edge-Erdős-Pósa property - Bruhn, Henning; Heinlein, Matthias; Joos, Felix (Arxiv, 2016)
We prove that the set of long cycles has the edge-Erdős-P\'osa property: for every fixed integer $\ell\ge 3$ and every $k\in\mathbb{N}$, every graph $G$ either contains $k$ edge-disjoint cycles of length at least $\ell$ (long cycles) or an edge set $X$ of size $O(k^2\log k + \ell k)$ such that $G-X$ does not contain any long cycle. This answers a question of Birmel\'e, Bondy, and Reed (Combinatorica 27 (2007), 135--145).
Identifizierung der Ressource nach: 30 May 2017
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