On computing a conditional edge-connectivity of a graph
Information Processing Letters
On the extraconnectivity of graphs
Discrete Mathematics - Special issue on combinatorics
On restricted edge-connectivity of graphs
Discrete Mathematics
Edge-cuts leaving components of order at least three
Discrete Mathematics
Super p-restricted edge connectivity of line graphs
Information Sciences: an International Journal
The k-Restricted Edge Connectivity of Balanced Bipartite Graphs
Graphs and Combinatorics
k-restricted edge-connectivity in triangle-free graphs
Discrete Applied Mathematics
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For a connected graph G, an edge set S is a k-restricted edge-cut if G-S is disconnected and every component of G-S has at least k vertices. Graphs that allow k-restricted edge-cuts are called @l"k-connected. The k-edge-degree of a graph G is the minimum number of edges between a connected subgraph H of order k and its complement G-H. A @l"k-connected graph is called @l"k-optimal if its k-restricted edge-connectivity equals its minimum k-edge-degree and super-@l"k if every minimum k-restricted edge-cut isolates a connected subgraph of order k. In this paper we consider the cases k=2 and k=3. For triangle-free graphs that are not @l"k-optimal, we establish lower bounds for the order of components left by a minimum k-restricted edge-cut in terms of the minimum k-edge-degree. Sufficient conditions for a triangle-free graph to be @l"k-optimal and super-@l"k follow.