Counterexamples to Thomassen's Conjecture on Decomposition of Cubic Graphs

Abstract

We construct an infinite family of counterexamples to Thomassen's conjecture that the vertices of every 3-connected, cubic graph on at least 8 vertices can be colored blue and red such that the blue subgraph has maximum degree at most 1 and the red subgraph minimum degree at least 1 and contains no path on 4 vertices.

Keywords

• Cubic graphs
• Thomassen's conjecture
• Graph decomposition