TY  - JOUR
ID  - Grzelec2025
LB  - Grzelec2025
AU  - Grzelec, Igor
AU  - Madaras, Tomáš
AU  - Onderko, Alfréd
TI  - On uniqueness of packing of three copies of 2-factors
ST  - On uniqueness of packing of three copies of 2-factors
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 1
SP  - 79
EP  - 101
DO  - https://doi.org/10.7494/OpMath.2025.45.1.79
UR  - https://doi.org/10.7494/OpMath.2025.45.1.79
AB  - 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.
KW  - uniquely packable graph
KW  - 2-factor
KW  - 3-packing
SN  - 1232-9274
ER  -