English

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.

Keywords

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}
}
R2 v1 2026-06-23T10:50:45.379Z