Counterexamples to Thomassen's conjecture on decomposition of cubic graphs

Thomas Bellitto, Tereza Klimošová, Martin Merker, Marcin Witkowski, Yelena Yuditsky

Published 2019-08-19Version 1

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.