2024/08/16 by Hongliang Lu, Yan Wang, Lu, Hongliang +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2408.08523
openalex publication_date 2024/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let m,n,r,s be nonnegative integers such that n≥ m=3r+s and 1≤ s≤ 3. Let δ(n,r,s)=\n2-(n-r)2 · amp;if s=1 ,
n2-(n-r+1)(n-r-1) · amp;if s=2,
n2 - (n-r)(n-r-1) · amp;if s=3.. We show that there exists a constant n0 > 0 such that if F1,…, Fn are 3-partite 3-graphs with n≥ n0 vertices in each partition class and minimum vertex degree of Fi is at least δ(n,r,s)+1 for i ∈ [n] then \F1,…,Fn\ admits a rainbow perfect matching. This generalizes a result of Lo and Markström on the vertex degree threshold for the existence of perfect matchings in 3-partite 3-graphs. In this proof, we use a fractional rainbow matching theory obtained by Aharoni et al. to find edge-disjoint fractional perfect matching.