$K_4$-subdivisions have the edge-Erdős-Pósa property

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-Erdős-Pósa property.

43 pages