$K_4$-subdivisions have the edge-Erd\H{o}s-P\'osa property

Henning Bruhn; Matthias Heinlein

$K_4$-subdivisions have the edge-Erd\H{o}s-P\'osa property

Combinatorics 2018-08-31 v1

Authors: Henning Bruhn , Matthias Heinlein

Abstract

We prove that every graph $G$ contains either $k$ edge-disjoint $K_4$ -subdivisions or a set $X$ of at most $O(k^8 \log k)$ edges such that $G-X$ does not contain any $K_4$ -subdivision. This shows that $K_4$ -subdivisions have the edge-Erd\H{o}s-P\'osa property.

Keywords

graph theory k4-subdivisions edge-erdos-posa property edge-disjoint extremal graph theory

Cite

@article{arxiv.1808.10380,
  title  = {$K_4$-subdivisions have the edge-Erd\H{o}s-P\'osa property},
  author = {Henning Bruhn and Matthias Heinlein},
  journal= {arXiv preprint arXiv:1808.10380},
  year   = {2018}
}

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43 pages

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