The boxicity of a graph G, denoted box(G), is the least integer d such that G is the intersection graph of a family of d-dimensional (axis-parallel) boxes. The cubicity, denoted cub(G), is the least d such that G is the intersection graph of a family of ...
The boxicity of a graph G = ( V , E ) is the least integer k for which there exist k interval graphs G i = ( V , E i ), 1 ≤ i ≤ k , such that $${E = E_1 \cap \cdots \cap E_k}$$ . Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and ...
A strong edge-coloring of a graph G is a function that assigns to each edge a color such that two edges within distance two apart must receive different colors. The minimum number of colors used in a strong edge-coloring is the strong chromatic index of ...
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