On recognizing Cartesian graph bundles

Graph bundles generalize the notion of covering graphs and graph products. In Imrich et al. (Discrete Math. 167/168 (1988) 393-403,) an algorithm that finds a presentation as a nontrivial Cartesian graph bundle for all graphs that are Cartesian graph bundles over triangle-free simple base was given. In this paper we extend this algorithm to recognize Cartesian graph bundles over a K-4\e-free simple base, without induced K-3,K-3. Finally, we conjecture the existence of algorithm for recognition of Cartesian graph bundle over a K-4/e-free simple base. (C) 2001 Elsevier Science B.V. All rights reserved.