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Towards a new framework for domination


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Author: Cáceres González, José
Márquez Pérez, Alberto
Morales, María
Puertas González, María Luz
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2011
Published in: Computers & Mathematics with Applications, 62 (1), 44-50.
Document type: Article
Abstract: Dominating concepts constitute a cornerstone in Graph Theory. Part of the efforts in the field have been focused in finding different mathematical frameworks where domination notions naturally arise, providing new points of view about the matter. In this paper, we introduce one of these frameworks based in convexity. The main idea consists of defining a convexity in a graph, already used in image processing, for which the usual parameters of convexity are closely related to domination parameters. Moreover, the Helly number of this convexity may be viewed as a new domination parameter whose study would be of interest.
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