Sphericity exceeds cubicity for almost all complete bipartite 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 certain graphs
Information Processing Letters
Sphericity, cubicity, and edge clique covers of graphs
Discrete Applied Mathematics
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A unit cube in k-dimension (or a k-cube) is defined as the Cartesian product R"1xR"2x...xR"k, where each R"i is a closed interval on the real line of the form [a"i,a"i+1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. Many NP-complete graph problems can be solved efficiently or have good approximation ratios in graphs of low cubicity. In most of these cases the first step is to get a low dimensional cube representation of the given graph. It is known that for a graph G, cub(G)=