Recognizing Graphs of Acyclic Cubical Complexes

Acyclic cubical complexes have first been introduced by Bandelt and Chepoi in analogy to acyclic simplicial complexes. They characterized them by cube contraction and elimination schemes and showed that the graphs of acyclic cubical complexes are retracts of cubes characterized by certain forbidden convex subgraphs. In this paper we present an algorithm of time complexity O(m log n) which recognizes whether a given graph G on n vertices with m edges is the graph of an acyclic cubical complex. This is significantly better than the complexity O(m √ n) of the fastest currently known algorithm for recognizing retracts of cubes in general.