Jones' Conjecture in subcubic graphs

TL;DR

This paper proves Jones' Conjecture for subcubic planar graphs, showing that if such a graph lacks $k+1$ disjoint cycles, then removing $2k$ vertices results in a forest, advancing understanding of graph cycle structures.

Contribution

The paper confirms Jones' Conjecture specifically for subcubic planar graphs, providing a significant extension of previous results in graph theory.

Findings

Subcubic planar graphs without $k+1$ disjoint cycles can be made acyclic by deleting $2k$ vertices.

The proof confirms the conjecture in a new class of graphs, expanding its applicability.

Results contribute to the understanding of cycle packing and vertex deletion in planar graphs.

Abstract

We confirm Jones' Conjecture for subcubic graphs. Namely, if a subcubic planar graph does not contain $k+1$ vertex-disjoint cycles, then it suffices to delete $2k$ vertices to obtain a forest.