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.
Bibliographical notePublisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.
- Cubic graphs
- Graph decomposition
- Thomassen’s conjecture