, Volume 16, Issue 2, pp 233-241

On a matroid defined by ear-decompositions of graphs

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A. Frank described in [1] an algorithm to determine the minimum number of edges in a graph G whose contraction leaves a factor-critical graph and he asked if there was an algorithm for the weighted version of the problem. We prove that the minimal critical-making edge-sets form the bases of a matroid and hence the matroid greedy algorithm gives rise to the desired algorithm.

Partially supported by OTKA F014919, OTKA T17181 and OTKA T17580.