Note: Sphericity, cubicity, and edge clique covers of graphs

Authors:
T. S. Michael;Thomas Quint
Affiliations:
Mathematics Department, United States Naval Academy, Annapolis, MD 21402, USA;Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, USA
Venue:
Discrete Applied Mathematics
Year:
2006

Citing 9
Cited 2

Sphericity exceeds cubicity for almost all complete bipartite graphs

Journal of Combinatorial Theory Series B
Embedding the n-cube in lower dimensions

European Journal of Combinatorics
On the sphericity of the graphs of semiregular polyhedra

Discrete Mathematics
The Johnson-Lindenstrauss Lemma and the sphericity of some graphs

Journal of Combinatorial Theory Series A
Geometrical embeddings of graphs

Discrete Mathematics
Unit disk graphs

Discrete Mathematics - Topics on domination
Unit disk graph recognition is NP-hard

Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Representing graphs by disks and balls (a survey of recognition-complexity results)

Discrete Mathematics
Sphere-of-influence graphs using the sup-norm

Mathematical and Computer Modelling: An International Journal

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

Graph Theory, Computational Intelligence and Thought
Cubicity, degeneracy, and crossing number

European Journal of Combinatorics

Quantified Score

Hi-index	0.04

Visualization

Abstract

The sphericity sph(G) of a graph G is the minimum dimension d for which G is the intersection graph of a family of congruent spheres in R^d. The edge clique cover number @q(G) is the minimum cardinality of a set of cliques (complete subgraphs) that covers all edges of G. We prove that if G has at least one edge, then sph(G)=