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- W2891698547 abstract "Let G = ( V , E ) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G . The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G . This problem is NP -hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP ( G ), which is the convex hull of the incidence vectors of the star forests of G . First, we prove several basic properties of SFP ( G ) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M -tree inequalities, for SFP ( G ). We show that for the case when G is a tree, the M -tree and the nonnegativity inequalities give a complete characterization of SFP ( G ). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [ Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP ( G ) when G is a cycle." @default.
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- W2891698547 date "2019-10-09" @default.
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- W2891698547 title "On the star forest polytope for trees and cycles" @default.
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- W2891698547 doi "https://doi.org/10.1051/ro/2018076" @default.
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