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On uniqueness of packing of three copies of 2-factors

Grzelec Igor, Madaras Tomáš, Onderko Alfréd

Opuscula Mathematica

2025

Vol. 45, no. 1

79--101

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 C3,C4,C5,C6 and 2C3 have no packing of three copies, C7,C8,C3∪C4,C4∪C4,C3∪C5 and 3C3 have unique packing, and any other collection of cycles has at least two distinct packings.