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 vertex-disjoint cycles, then it suffices to delete 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}
}