Sufficient conditions for maximally edge-connected and super-edge-connected

Document Type : Original paper


1 RWTH Aachen University

2 Anhui University of Finance and Economics


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.


Main Subjects

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