Counterexamples to Thomassen’s Conjecture on Decomposition of Cubic Graphs

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)2595-2599
Number of pages5
JournalGraphs and Combinatorics
Issue number6
StatePublished - 1 Nov 2021


  • Cubic graphs
  • Graph decomposition
  • Thomassen’s conjecture

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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