par Esperet, Louis;Joret, Gwenaël 
Référence Graphs and combinatorics, 29, 3, page (417-427)
Publication Publié, 2013-05
Référence Graphs and combinatorics, 29, 3, page (417-427)
Publication Publié, 2013-05
Article révisé par les pairs
| Résumé : | The boxicity of a graph G = (V, E) is the least integer k for which there exist k interval graphs Gi = (V, Ei), 1 ≤ i ≤ k, such that E = E1∩... ∩Ek. Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface Σ of genus g is at most 5g + 3. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces. © 2012 Springer. |
