@Article{Grzelec2025,
author = "Grzelec, Igor and Madaras, Tomáš and Onderko, Alfréd",
title = "On uniqueness of packing of three copies of 2-factors",
journal = "Opuscula Math.",
year = "2025",
volume = "45",
number = "1",
pages = "79--101",
doi = "https://doi.org/10.7494/OpMath.2025.45.1.79",
url = "https://doi.org/10.7494/OpMath.2025.45.1.79",
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.",
keywords = "uniquely packable graph, 2-factor, 3-packing",
issn = "1232-9274"
}