The perfectly Matchable Subgraph Polytope of an arbitrary graph

Abstract

The Perfectly Matchable Subgraph Polytope of a graphG=(V, E), denoted byPMS(G), is the convex hull of the incidence vectors of thoseX⫅V which induce a subgraph having a perfect matching. We describe a linear system whose solution set isPMS(G), for a general (nonbipartite) graphG. We show how it can be derived via a projection technique from Edmonds' characterization of the matching polytope ofG. We also show that this system can be deduced from the earlier bipartite case [2], by using the Edmonds-Gallai structure theorem. Finally, we characterize which inequalities are facet inducing forPMS(G), and hence essential.

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Balas, E., Pulleyblank, W.R. The perfectly Matchable Subgraph Polytope of an arbitrary graph. Combinatorica 9, 321–337 (1989). https://doi.org/10.1007/BF02125345

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AMS subject classification (1980)

  • 52A25
  • 05C70