2020/04/27 by Hongliang Lu, Yan Wang, Lu, Hongliang +3 · 3 citations
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Graph Theory Research #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2004.12561
Aharoni and Howard conjectured that, for positive integers n,k,t with n≥ k and n≥ t, if F1,…, Ft⊆ [n]\choose k such that |Fi|>n\choose k-n-t+1\choose k for i∈ [t] then there exist ei∈ Fi for i∈ [t] such that e1,…,et are pairwise disjoint. Huang, Loh, and Sudakov proved this conjecture for t