On maximal independent sets of vertices in claw-free graphs

  title={On maximal independent sets of vertices in claw-free graphs},
  author={George J. Minty},
  journal={J. Comb. Theory, Ser. B},
  • G. Minty
  • Published 1980
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
Abstract A graph is claw-free if: whenever three (distinct) vertices are joined to a single vertex, those three vertices are a nonindependent (nonstable) set. Given a finite claw-free graph with real numbers (weights) assigned to the vertices, we exhibit an algorithm for producing an independent set of vertices of maximum total weight. This algorithm is “efficient” in the sense of J. Edmonds, that is to say, the number of computational steps required is of polynomial (not exponential or… Expand
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