On critically k-edge-connected graphs.
K. Budayasa, Lou Caccetta · 1990
Abstract: Let G be a simple graph on n vertices having edge-connectivity /(. ' (G)> a and minimum degree o(G) We say G is k-critical if /(. ' (G) = k and /(. ' (G- e) < k for every edge e of G. In this paper we prove that a k-critical graph has 1< ' (G) o(G). We descri be a number of classes of k-cri tical graphs and consider the problem of determining the edge-maximal ones. 1.