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.
Original language | English |
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Journal | Graphs and Combinatorics |
Volume | 37 |
Issue number | 6 |
Pages (from-to) | 2595-2599 |
ISSN | 0911-0119 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Cubic graphs
- Graph decomposition
- Thomassen’s conjecture