English

Jones' conjecture for Halin graphs and a bit more

Combinatorics 2026-03-02 v3

Abstract

We prove Jones' famous conjecture for Halin graphs and a somewhat more general class of graphs, too. A based planar graph is a planar one that has a face adjacent to every other face. We confirm Jones' conjecture for based planar graphs. Namely, if a based planar graph does not contain k+1k+1 vertex-disjoint cycles, then it suffices to delete 2k2k vertices to make it acyclic.

Keywords

Cite

@article{arxiv.2401.07376,
  title  = {Jones' conjecture for Halin graphs and a bit more},
  author = {Pál Bärnkopf and Ervin Győri},
  journal= {arXiv preprint arXiv:2401.07376},
  year   = {2026}
}
R2 v1 2026-06-28T14:16:30.698Z