On the cubicity of certain graphs

Authors:
L. S. Chandran;C. Mannino;G. Oriolo
Affiliations:
Max-Planck Institute for Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany;Dipartimento di Informatica e Sistemistica, Università La Sapienza, Via Buonarroti 12, 00185 Roma, Italy;Dipartimento di Informatica Sistemi e Produzione, Università di Tor Vergata, Via del Politecnico 1, 00133 Roma, Italy
Venue:
Information Processing Letters
Year:
2005

Citing 3
Cited 1

Interval representations of planar graphs

Journal of Combinatorial Theory Series B
Grid intersection graphs and boxicity

Discrete Mathematics - Special issue on combinatorics and algorithms
A special planar satisfiability problem and a consequence of its NP-completeness

Discrete Applied Mathematics

On the Cubicity of AT-Free Graphs and Circular-Arc Graphs

Graph Theory, Computational Intelligence and Thought

Quantified Score

Hi-index	0.89

Visualization

Abstract

The boxicity of a graph G is the minimum dimension b such that G is representable as the intersection graph of axis-parallel boxes in the b-dimensional space. When the boxes are restricted to be axis-parallel b-dimensional cubes, the minimum dimension b required to represent G is called the cubicity of G. In this paper we show that cubicity(H"d)==(d-1)/(logd). We also show that (1) cubicity(G)=(log@a)/(log(D+1)), (2) cubicity(G)=(logn-log@w)/(logD), where @a,@w,D and n denote the stability number, the clique number, the diameter and the number of vertices of G. As consequences of these lower bounds we provide lower bounds for the cubicity of planar graphs, bipartite graphs, triangle-free graphs, etc., in terms of their diameter and the number of vertices.