2018/02/24 by Tian, Yingzhi, Xu, Liqiong, Lai, Hong-Jian +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1802.08843
Let H=(V,E) be a hypergraph, where V is a set of vertices and E is a set of non-empty subsets of V called edges. If all edges of H have the same cardinality r, then H is a r-uniform hypergraph; if E consists of all r-subsets of V, then H is a complete r-uniform hypergraph, denoted by Knr, where n=|V|. A hypergraph H'=(V',E') is called a subhypergraph of H=(V,E) if V'⊆ V and E'⊆ E. A r-uniform hypergraph H=(V,E) is k-edge-maximal if every subhypergraph of H has edge-connectivity at most k, but for any edge e∈ E(Knr)∖ E(H), H+e contains at least one subhypergraph with edge-connectivity at least k+1. Let k and r be integers with k≥2 and r≥2, and let t=t(k,r) be the largest integer such that (t-1r-1)≤ k. That is, t is the integer satisfies (t-1r-1)≤ k