Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21282120170601Sufficient conditions for maximally edge-connected and super-edge-connected35411359410.22049/cco.2017.13594ENLutzVolkmannRWTH Aachen University0000-0003-3496-277XZhen-MuHongAnhui University of Finance and EconomicsJournal Article20161012Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph is maximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is maximally edge-connected or super-edge-connected if the number of edges is large enough.http://comb-opt.azaruniv.ac.ir/article_13594_f13dab4717cdbf819f2dae83f101834a.pdf