Algorithm for recognizing Cartesian graph bundlesZmazek, Blaž (Avtor) Žerovnik, Janez (Avtor) matematikateorija grafovkartezični grafovski svežnjienolična lokalna produktna lastnostosnovna faktorizacijarazpoznavanjepolinomski algoritemmathematicsgraph theoryCartesian graph bundlesunique square propertyfundamental factorizationpolynomial algorithmrecognitionGraph bundles generalize the notion of covering graphs and graphs products. Authors W. Imrich, T. Pisanski and J. Žerovnik constructed 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 (Discrete Math. 167, 168 (1998) 393-403). The uniquesquare property is defined in Discrete Math., 244 (2002) 551-561, and it is shown that any equivalence relation possesing the unique square property determines the fundamental factorization of a graph as a nontrivial Cartesian graph bundle over arbitrary base graph. In this paper we define the relation ▫$Delta$▫ having the unique square property on Cartesian graph bundles over ▫$K_4 setminus e$▫-free simple base. We also give a polynomial algorithm for recognizing Cartesian graph bundles over ▫$K_4 setminus e$▫-simple base.19992015-07-10 14:52:37Članek v reviji51506sl