@inproceedings{3e6f8653e6d4463ab2c395ac2251c825,
title = "A polyhedral view to generalized multiple domination and limited packing",
abstract = "Given an undirected simple graph G = (V,E) and integer values fv, v ∈ V, a node subset D ⊆ V is called an f-tuple dominating set if, for each node v ∈ V, its closed neighborhood intersects D in at least fv nodes. We investigate the polyhedral structure of the polytope that is defined as the convex hull of the incidence vectors in RV 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.",
author = "Jos{\'e} Neto",
note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.; 5th International Symposium on Combinatorial Optimization, ISCO 2018 ; Conference date: 11-04-2018 Through 13-04-2018",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/978-3-319-96151-4\_30",
language = "English",
isbn = "9783319961507",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "352--363",
editor = "Giovanni Rinaldi and Mahjoub, \{A. Ridha\} and Jon Lee",
booktitle = "Combinatorial Optimization - 5th International Symposium, ISCO 2018, Revised Selected Papers",
}