Counterexamples to Thomassen's conjecture on decomposition of cubic graphs
Combinatorics
2019-08-20 v1
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.
Cite
@article{arxiv.1908.06697,
title = {Counterexamples to Thomassen's conjecture on decomposition of cubic graphs},
author = {Thomas Bellitto and Tereza Klimošová and Martin Merker and Marcin Witkowski and Yelena Yuditsky},
journal= {arXiv preprint arXiv:1908.06697},
year = {2019}
}