Abstract
Given an undirected simple graph \(G=(V,E)\) and integer values \(f_v, v\in V\), a node subset \(D\subseteq V\) is called an f-tuple dominating set if, for each node \(v\in V\), its closed neighborhood intersects D in at least \(f_v\) nodes. We investigate the polyhedral structure of the polytope that is defined as the convex hull of the incidence vectors in \(\mathbb {R}^{V}\) of the f-tuple dominating sets in G. We provide a complete formulation for the case of stars and introduce a new family of (generally exponentially many) inequalities which are valid for the f-tuple dominating set polytope and that can be separated in polynomial time. A corollary of our results is a proof that a conjecture present in the literature on a complete formulation of the 2-tuple dominating set polytope of trees does not hold. Investigations on adjacency properties in the 1-skeleton of the f-tuple dominating set polytope are also reported.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
