Arboricity and subgraph listing algorithms
SIAM Journal on Computing
Introduction to algorithms
Quasi-median graphs and algebras
Journal of Graph Theory
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
Recognizing median graphs in subquadratic time
Theoretical Computer Science
Median Graphs and Triangle-Free Graphs
SIAM Journal on Discrete Mathematics
Journal of Graph Theory
Characterizing almost-median graphs
European Journal of Combinatorics
Recognizing partial cubes in quadratic time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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Isometric subgraphs of hypercubes, or partial cubes as they are also called, are a rich class of graphs that include median graphs, subdivision graphs of complete graphs, and classes of graphs arising in mathematical chemistry and biology. In general, one can recognize whether a graph on n vertices and m edges is a partial cube in O(mn) steps, faster recognition algorithms are only known for median graphs. This paper exhibits classes of partial cubes that are not median graphs but can be recognized in O(mlogn) steps. On the way relevant decomposition theorems for partial cubes are derived, one of them correcting an error in a previous paper (Eur. J. Combin. 19 (1998) 677).