On a matroid defined by ear-decompositions of graphs

Abstract

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.

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References

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

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Szigeti, Z. On a matroid defined by ear-decompositions of graphs. Combinatorica 16, 233–241 (1996). https://doi.org/10.1007/BF01844849

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Mathematics Subject Classification (1991)

  • 05 C 70
  • 05 C 75