Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2 1 2017 06 01 Sufficient conditions for maximally edge-connected and super-edge-connected 35 41 13594 10.22049/cco.2017.13594 EN Lutz Volkmann RWTH Aachen University Zhen-Mu Hong Anhui University of Finance and Economics Journal Article 2016 10 12 Let $G$ 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. https://comb-opt.azaruniv.ac.ir/article_13594_f13dab4717cdbf819f2dae83f101834a.pdf