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• W2897721402 abstract "Given an undirected simple graph G with node set V and edge set E, let $$f_v$$ , for each node $$v in V$$ , denote a nonnegative integer value that is lower than or equal to the degree of v in G. An f-dominating set in G is a node subset D such that for each node $$vin V{{setminus }}D$$ at least $$f_v$$ of its neighbors belong to D. In this paper, we study the polyhedral structure of the polytope defined as the convex hull of all the incidence vectors of f-dominating sets in G and give a complete description for the case of trees. We prove that the corresponding separation problem can be solved in polynomial time. In addition, we present a linear-time algorithm to solve the weighted version of the problem on trees: Given a cost $$c_vin {mathbb {R}}$$ for each node $$vin V$$ , find an f-dominating set D in G whose cost, given by $$sum _{vin D}{c_v}$$ , is a minimum." @default.
• W2897721402 created "2018-10-26" @default.
• W2897721402 creator A5016707389 @default.
• W2897721402 creator A5086489073 @default.
• W2897721402 date "2018-10-20" @default.
• W2897721402 modified "2023-09-25" @default.
• W2897721402 title "On f-domination: polyhedral and algorithmic results" @default.
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• W2897721402 doi "https://doi.org/10.1007/s00186-018-0650-4" @default.
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