A note on the 1-factorization of non-uniform complete hypergraph

Taijiang Jiang, Qiang Sun and Chao Zhang

Applied Mathematics and Computation, 2025, vol. 485, issue C

Abstract: Given G=(g1,⋯,gt) with gi∈N for 1≤i≤t, let GKs≤t denote the non-uniform complete hypergraph on s vertices, whose edge set contains gi copies of every i-subset of vertex set for 1≤i≤t. Let Ks≤t denote GKs≤t for gi=1 for 1≤i≤t. Recently, He et al. determined all s,t such that Ks≤t has a 1-factorization. In this manuscript, we consider the 1-factorization of GKs≤t and obtain the following results. (1) If 2gt≥gj for 1≤j≤t−1 and s≡0(modt), then GKs≤t has a 1-factorization for sufficiently large s. (2) If GKs≤t has a 1-factorization for sufficiently large s, then s≡0,−1(modt).

Keywords: Hypergraph; 1-factorization (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:485:y:2025:i:c:s0096300324004685

DOI: 10.1016/j.amc.2024.129007

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