Minimum ℓ-degree thresholds for rainbow perfect matching in k-uniform hypergraphs

2023/06/16 by You Jie, You, Jie
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2306.09796

openalex publication_date 2023/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given n∈ kℕ elements set V and k-uniform hypergraphs H₁,…,H_n/k on V. A rainbow perfect matching is a collection of pairwise disjoint edges E₁∈ H₁,…,E_n/k∈ H_n/k such that E₁∪⋯∪ E_n/k=V. In this paper, we determine the minimum ℓ-degree condition that guarantees the existence of a rainbow perfect matching for sufficiently large n and ℓ≥ k/2.

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