On uniqueness of packing of three copies of 2-factors

Fuente: arXiv
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Autori principali: Grzelec, Igor, Madaras, Tomáš, Onderko, Alfréd
Natura: Preprint
Pubblicazione: 2024
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author Grzelec, Igor
Madaras, Tomáš
Onderko, Alfréd
author_facet Grzelec, Igor
Madaras, Tomáš
Onderko, Alfréd
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_11721
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On uniqueness of packing of three copies of 2-factors
Grzelec, Igor
Madaras, Tomáš
Onderko, Alfréd
Combinatorics
05c70
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.
title On uniqueness of packing of three copies of 2-factors
topic Combinatorics
05c70
url https://arxiv.org/abs/2403.11721