Factoring a graph in polynomial time
European Journal of Combinatorics
The maximum genus of graph bundles
European Journal of Combinatorics
Journal of Graph Theory
Factoring Cartesian-product graphs
Journal of Graph Theory
The chromatic numbers of graph bundles over cycles
Selected papers of the 14th British conference on Combinatorial conference
Journal of Graph Theory
Recognizing Cartesian graph bundles
Discrete Mathematics
Recognizing Graph Products and Bundles
SOFSEM '96 Proceedings of the 23rd Seminar on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Algorithm for recognizing Cartesian graph bundles
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Algorithm for recognizing Cartesian graph bundles
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
The edge fault-diameter of Cartesian graph bundles
European Journal of Combinatorics
Fault diameters of graph products and bundles
ICCOMP'10 Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference - Volume II
Mixed fault diameter of Cartesian graph bundles
Discrete Applied Mathematics
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Graph bundles generalize the notion of covering graphs and graph products. In Imrich et al. (Discrete Math. 167/168 (1998) 393) authors 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 using the relation δ* having the square property. An equivalence relation R on the edge set of a graph has the (unique) square property if and only if any pair of adjacent edges which belong to distinct R-equivalence classes span exactly one induced 4-cycle (with opposite edges in the same R-equivalence class). In this paper we define the unique square property and show that any weakly 2-convex equivalence relation possessing the unique square property determines the fundamental factorization of a graph as a nontrivial cartesian graph bundle over an arbitrary base graph, whenever it separates degenerate and nondegenerate edges of the factorization.