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Article Dans Une Revue Discrete Applied Mathematics Année : 2022

A polyhedral view to a generalization of multiple domination

Résumé

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 study the polytope that is defined as the convex hull of the incidence vectors in RV of the f -tuple dominating sets in G. New families of valid inequalities are introduced and a complete formulation is given for the case of stars. A corollary of our results is a proof that the conjecture reported in Argiroffo (2013) on a complete formulation of the 2-tuple dominating set polytope of trees does not hold. Preliminary computational results are also reported.

Dates et versions

hal-03579253 , version 1 (18-02-2022)

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Citer

José Neto. A polyhedral view to a generalization of multiple domination. Discrete Applied Mathematics, 2022, 313, pp.1-17. ⟨10.1016/j.dam.2022.01.011⟩. ⟨hal-03579253⟩
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