Hoffmann-Ostenhof's 3-Decomposition Conjecture
Let be a connected cubic graph. Hoffmann-Ostenhof's 3-Decomposition Conjecture. can be decomposed into a spanning tree, a collection of cycles, and a possibly empty matching. This conjecture is also known as the 3-Decomposition Conjecture and is equivalent to the 2-Decomposition Conjecture. It is known for several classes of cubic graphs, including planar cubic graphs, cubic traceable graphs, and claw-free cubic graphs, but remains open in general.
References
Primary source
F. Botler, A. Jiménez, M. Sambinelli and Y. Wakabayashi, “On the structure of a smallest counterexample and a new class verifying the 2-Decomposition Conjecture”, arXiv:2309.09345 (2023).
Additional references
2 papers in this index state this conjecture (2016–2023). The statement above is taken from the most recent of them; the others are arXiv:1607.04768.
Progress summary
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Solutions 0
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