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

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

##### چکیده

Let \$G\$ be a connected graph with minimum degree \$delta\$ and edge-connectivity \$lambda\$. A graph ismaximally edge-connected if \$lambda=delta\$, and it is super-edge-connected if every minimum edge-cut istrivial; 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 maximallyedge-connected or super-edge-connected if the numberof edges is large enough. Examples will demonstrate that our conditions are sharp.noindent {bf Keywords:} Edge-connectivity; Maximally edge-connected graphs; Super-edge-connectedgraphs

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عنوان ژورنال:

دوره 2  شماره 1

صفحات  35- 41

تاریخ انتشار 2017-06-01

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