On uniqueness of packing of three copies of 2-factors

Igor Grzelec; Tomáš Madaras; Alfréd Onderko

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arXiv · 2403.11721

On uniqueness of packing of three copies of 2-factors

Igor Grzelec·Tomáš Madaras·Alfréd Onderko

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Abstract

The packing of three copies of a graph $G$ is the union of three edge-disjoint copies (with the same vertex set) of $G$. In this paper, we completely solve the problem of the uniqueness of packing of three copies of 2-regular graphs. In particular, we show that $C_3,C_4,C_5,C_6$ and $2C_3$ have no packing of three copies, $C_7,C_8,C_3 \cup C_4, C_4 \cup C_4, C_3 \cup C_5$ and $3C_3$ have unique packing, and any other collection of cycles has at least two distinct packings.

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BibTeX RIS

Igor Grzelec, Tomáš Madaras, Alfréd Onderko. 2024-03-18. On uniqueness of packing of three copies of 2-factors. https://arxiv.org/abs/2403.11721

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