We prove that every graph on edges has boxicity, and that there are examples showing that this bound is asymptotically best possible.

Mar 19, 2015 · We use this result to study the connection between the boxicity of graphs and their Colin de Verdière invariant, which share many similarities.

Abstract. The boxicity of a graph G = (V,E) is the smallest integer k for which there exist k interval graphs Gi = (V,Ei), 1 ≤ i ≤ k, such that E = E1 ...

Abstract. The boxicity of a graph G = ( V , E ) G V E G=(V,E) is the smallest integer k k k for which there exist k k k interval graphs G i = ( V , E i ) ...

We use this result to study the connection between the boxicity of graphs and their Colin de Verdière invariant, which share many similarities. Known results ...

The boxicity of a graph G = ( V , E ) is the smallest integer k for which there exist k interval graphs G i = ( V , E i ) , 1 ≤ i ≤ k , such that E = E 1 ...

Aug 28, 2015 · Outerplanar graphs have boxicity at most 2 (Scheinerman 1984). Planar graphs have boxicity at most 3 (Thomassen 1986).

We use this result to study the connection between the boxicity of graphs and their Colin de Verdi\`ere invariant, which share many similarities. Known results ...

The boxicity of a graph $G=(V,E)$ is the smallest integer $k$ for which there exist $k$ interval graphs $G_i=(V,E_i)$, $1 \le i \le k$, such that $E=E_1 ...

The boxicity of a graph is the minimum dimension in which a given graph can be represented as an intersection graph of axis-parallel boxes.