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Completion and decomposition of hypergraphs into dominating sets of graphs

Author
Martí, J.; Mora, M.; Ruiz, J.L.
Type of activity
Journal article
Journal
Electronic notes in discrete mathematics
Date of publication
2015-11
Volume
49
First page
213
Last page
220
DOI
https://doi.org/10.1016/j.endm.2015.06.031 Open in new window
Repository
http://hdl.handle.net/2117/81940 Open in new window
Abstract
The collection of the vertex dominating sets of a graph defines a hypergraph on the set of vertices of the graph. However, there are hypergraphs H that are not the collection of the vertex dominating sets of any graph. This paper deals with the question of completing these hypergraphs H to the vertex dominating sets of some graphs G. We demonstrate that such graphs G exist and, in addition, we prove that these graphs define a poset whose minimal elements provide a decomposition of H. Moreover, w...
Citation
Martí-Farré, J., Mora, M., Ruiz, J. Completion and decomposition of hypergraphs into dominating sets of graphs. "Electronic notes in discrete mathematics", Novembre 2015, vol. 49, p. 213-220.
Keywords
Graph, dominating set, hypergraph
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications
DCG - Discrete and Combinatorial Geometry

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