par Cardinal, Jean 
;Felsner, Stefan
Référence Lecture notes in computer science, 8845, page (1-13)
Publication Publié, 2014
;Felsner, StefanRéférence Lecture notes in computer science, 8845, page (1-13)
Publication Publié, 2014
Article révisé par les pairs
| Résumé : | A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of a hypercube in which the graph can be embedded. We consider the problem of covering the vertices of a partial cube with the minimum number of zones. The problem admits several special cases, among which are the problem of covering the cells of a line arrangement with a minimum number of lines, and the problem of finding a minimum-size fibre in a bipartite poset. For several such special cases, we give upper and lower bounds on the minimum size of a covering by zones. We also consider the computational complexity of those problems, and establish some hardness results. |
