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A subset S of vertices of a graph G=(V,E) is P 3 -convex if every simple path of three vertices starting and ending in S is contained in S. The P 3 -convex hull of S is the smallest P 3 -convex set containing S and the P 3 -hull number of G is the minimum number of vertices of a subset S such that its convex hull is V. It is a known fact that the calculation of the P 3 -hull number of a graph is NP-hard. In the present work we start the study of this problem from a polyhedral point of view, that is, we pose it as a binary IP problem and we study the associated polytope by exploring several families of facet-defining inequalities. © 2018 Elsevier B.V.


Documento: Artículo
Título:Computing the P 3 -hull number of a graph, a polyhedral approach
Autor:Blaum, M.; Marenco, J.
Filiación:Instituto de Ciencias, Universidad Nacional de General Sarmiento, Buenos Aires, Argentina
Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Combinatorial optimization; Discrete convexity; Facet-defining inequalities; Hull number; Combinatorial optimization; Computational geometry; Set theory; Convex hull; Convex set; Discrete convexity; Facet-defining inequalities; Hull number; NP-hard; Polyhedral approach; Polytopes; Graph theory
Página de inicio:155
Página de fin:166
Título revista:Discrete Applied Mathematics
Título revista abreviado:Discrete Appl Math


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---------- APA ----------
Blaum, M. & Marenco, J. (2019) . Computing the P 3 -hull number of a graph, a polyhedral approach. Discrete Applied Mathematics, 255, 155-166.
---------- CHICAGO ----------
Blaum, M., Marenco, J. "Computing the P 3 -hull number of a graph, a polyhedral approach" . Discrete Applied Mathematics 255 (2019) : 155-166.
---------- MLA ----------
Blaum, M., Marenco, J. "Computing the P 3 -hull number of a graph, a polyhedral approach" . Discrete Applied Mathematics, vol. 255, 2019, pp. 155-166.
---------- VANCOUVER ----------
Blaum, M., Marenco, J. Computing the P 3 -hull number of a graph, a polyhedral approach. Discrete Appl Math. 2019;255:155-166.