Abstract
A setE′ ofk edges in a multigraphG=(V,E) is said to be ak most vital edge set (k-MVE set) if these edges being removed fromG, the resultant graphG′=(V,E −E′) has minimum number of spanning trees. The problem of finding ak-MVE set for two-terminal series-parallel graphs is considered in this paper. We present anO (|E|) time algorithm for the casek=1, and anO(|V| k +|E|) time algorithm for arbitraryk.
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