Abstract
The cut polytopeP C (G) of a graphG=(V, E) is the convex hull of the incidence vectors of all edge sets of cuts ofG. We show some classes of facet-defining inequalities ofP C (G). We describe three methods with which new facet-defining inequalities ofP C (G) can be constructed from known ones. In particular, we show that inequalities associated with chordless cycles define facets of this polytope; moreover, for these inequalities a polynomial algorithm to solve the separation problem is presented. We characterize the facet defining inequalities ofP C (G) ifG is not contractible toK 5. We give a simple characterization of adjacency inP C (G) and prove that for complete graphs this polytope has diameter one and thatP C (G) has the Hirsch property. A relationship betweenP C (G) and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied.
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The research of this author was performed at the Institut fur Operations Research, Universität Bonn, West Germany, and supported by the Alexander von Humbold Stiftung.
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Barahona, F., Mahjoub, A.R. On the cut polytope. Mathematical Programming 36, 157–173 (1986). https://doi.org/10.1007/BF02592023
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DOI: https://doi.org/10.1007/BF02592023