Boxicity of graphs with bounded degree

Louis Esperet (1)

1 G-SCOP_OC - Optimisation Combinatoire

The boxicity of a graph G = (V, E) is the smallest k for which there exist k interval graphs G(i) = (V, E(i)), 1 <= i <= k, such that E = E(1) boolean AND ... boolean AND E(k). Graphs with boxicity at most d are exactly the intersection graphs of (axis-parallel) boxes in R(d). In this note, we prove that graphs with maximum degree Delta have boxicity at most Delta(2) + 2, which improves the previous bound of 2 Delta(2) obtained by Chandran et al.

Domaines: Mathématique discrète [cs.DM]

Louis Esperet. Boxicity of graphs with bounded degree. European Journal of Combinatorics, 2009, 30 (5), pp.1277-1280. ⟨10.1016/j.ejc.2008.10.003⟩. ⟨hal-00451866⟩