Cut dominants and forbidden minors
Combinatorics
2015-02-27 v1
Abstract
The cut dominant of a graph is the unbounded polyhedron whose points are all those that dominate some convex combination of proper cuts. Minimizing a nonnegative linear function over the cut dominant is equivalent to finding a minimum weight cut in the graph. We give a forbidden-minor characterization of the graphs whose cut dominant can be defined by inequalities with integer coefficients and right-hand side at most 2. Our result is related to the forbidden-minor characterization of TSP-perfect graphs by Fonlupt and Naddef (Math. Prog., 1992). We prove that our result implies theirs, with a shorter proof. Furthermore, we establish general properties of forbidden minors for right-hand sides larger than 2.
Cite
@article{arxiv.1502.07714,
title = {Cut dominants and forbidden minors},
author = {Michele Conforti and Samuel Fiorini and Kanstantsin Pashkovich},
journal= {arXiv preprint arXiv:1502.07714},
year = {2015}
}