Degree conditions for restricted-edge-connectivity and isoperimetric-edge-connectivity to be optimal

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Degree conditions for restricted-edge-connectivity and isoperimetric-edge-connectivity to be optimal

For a connected graphG= (V ,E), an edge set S ⊂ E is a k-restricted-edge-cut, ifG−S is disconnected and every component of G− S has at least k vertices. The k-restricted-edge-connectivity of G, denoted by k(G), is defined as the cardinality of a minimum k-restricted-edge-cut. The k-isoperimetric-edge-connectivity is defined as k(G)=min{|[U,U ]| : U ⊂ V, |U | k, |U | k}, where [U,U ] is the set ...

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Let G = (V, E) be a connected graph. Let G = (V, E) be a connected graph. An edge set F ⊂ E is said to be a k-restricted edge cut, if G− F is disconnected and every component of G− F has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k-restricted edge cut of G. A graph G is λk-connected, if G contains a k-restricted edge cut. A λk...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2007

ISSN: 0012-365X

DOI: 10.1016/j.disc.2006.06.028