Clique graphs and Helly graphs
Journal of Combinatorial Theory Series B
Superextensions and the depth of median graphs
Journal of Combinatorial Theory Series A
Clique Graphs of Chordal and Path Graphs
SIAM Journal on Discrete Mathematics
Graphs of acyclic cubical complexes
European Journal of Combinatorics - Special issue on discrete metric spaces
A convexity lemma and expansion procedures for bipartite graphs
European Journal of Combinatorics
SIAM Journal on Discrete Mathematics
Graph classes: a survey
Partial hamming graphs and expansion procedures
Discrete Mathematics
Navigating in a Graph by Aid of Its Spanning Tree Metric
SIAM Journal on Discrete Mathematics
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In this paper we consider cube graphs, that is intersection graphs of maximal hypercubes of graphs. In contrast to the related concepts of line graphs and clique graphs, we show that any graph is a cube graph of a (bipartite) graph. We answer a question of Bandelt and Chepoi (European J. Combin. 17 (1996) 113) by showing that dually chordal graphs are precisely cube graphs of graphs of acyclic cubical complexes. Similarly, we characterize classes of chordal graphs, Helly chordal graphs and doubly chordal graphs as cube graphs of certain subclasses of isometric subgraphs of hypercubes.