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 θ ( 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 ) ⩽ θ ( G ) . Our upper bound remains valid for intersection graphs defined by balls in the L p -norm for 1 ⩽ p ⩽ ∞ .
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