On uniqueness of packing of three copies of 2-factors
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 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.
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