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

TL;DR

This paper proves that in any graph, either there are k edge-disjoint subdivisions of K4 or a small set of edges whose removal eliminates all such subdivisions, establishing the edge-Erdős-Pósa property for K4-subdivisions.

Contribution

It demonstrates that K4-subdivisions possess the edge-Erdős-Pósa property with a specific bound on the size of the edge set needed for elimination.

Findings

Existence of either k edge-disjoint K4-subdivisions or a small edge set removing all K4-subdivisions.

Bound of O(k^8 log k) edges for the removal set.

Confirmation that K4-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-Erd\H{o}s-P\'osa property.