2023/07/25 by Barbara Maenhaut, Maenhaut, Barbara, Jeremy Mitchell +3
Computer Science · Engineering · #05C51 #05E18 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2307.13196
openalex publication_date 2023/07/25 · openalex created_date 2023/07/27 · openalex updated_date 2026/07/28
A connected 1-factorisation is a 1-factorisation of a hypergraph for which the union of each pair of distinct 1-factors is a connected hypergraph. A uniform 1-factorisation is a 1-factorisation of a hypergraph for which the union of each pair of distinct 1-factors is isomorphic to the same subhypergraph, and a uniform-connected 1-factorisation is a uniform 1-factorisation in which that subhypergraph is connected. Chen and Lu [Journal of Algebraic Combinatorics, 46(2) 475--497, 2017] describe a family of 1-factorisations of the complete 3-uniform hypergraph on q+1 vertices, where q≡ 2\pmod 3 is a prime power. In this paper, we show that their construction yields a connected 1-factorisation only when q=2,5,11 or q=2p for some odd prime p, and a uniform 1-factorisation only for q=2,5,8 (each of these is a uniform-connected 1-factorisation).