On uniqueness of packing of three copies of 2-factors

2024/03/18 by Igor Grzelec, Grzelec, Igor, Tomáš Madaras +3
Engineering · Mathematics · #05c70 #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Optimization and Packing Problems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2403.11721

openalex publication_date 2024/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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