Boxicity of Graphs on Surfaces

Louis Esperet, Gwenaël Joret
2012 Graphs and Combinatorics  
The boxicity of a graph G=(V,E) is the least integer k for which there exist k interval graphs G_i=(V,E_i), 1 < i < k, such that E=E_1 ∩ ... ∩ E_k. 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
more » ... he dimension of the adjacency poset of graphs on surfaces.
doi:10.1007/s00373-012-1130-x fatcat:arahokwfj5eevmjhzutkrgfq3y