Intersection graphs of maximal hypercubes
A hypercube \(Q_k\) is the graph with vertex set \(\{0,1\}^k\) where two vertices are adjacent whenever they differ in exactly one position. The cube graph \(Q(G)\) of a graph \(G\) is the intersection graph of maximal (induced) hypercubes of \(G\): The vertices of \(Q(G)\) correspond to the maximal hypercubes of \(G\), and two vertices are adjacent if the corresponding hypercubes are nondisjoint. The author investiges the cube graphs of several particular graph classes. Among other results, he proves that any graph is a cube graph of a bipartite graph, and that dually chordal graphs are exactly the cube graphs of graphs of acyclic cubical complexes.
scientific article; zbMATH DE number 1891298
scientific article