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 3connected, 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.06697
 Bibcode:
 2019arXiv190806697B
 Keywords:

 Mathematics  Combinatorics