Algorithm for recognizing Cartesian graph bundles

Authors:
Blaz˘ Zmazek;Janez Z˘erovnik
Affiliations:
University of Maribor, FS, Smetanova 17, 2000 Maribor, Slovenia and Department of Theoretical Computer Science, Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1111 Ljubljana, Slove ...;University of Maribor, FS, Smetanova 17, 2000 Maribor, Slovenia
Venue:
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Year:
2002

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Abstract

Graph bundles generalize the notion of covering graphs and graph products. In [8], 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. In [21], the unique square property is defined and it is shown that any equivalence relation possessing 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 a relation Δ having a unique square property on Cartesian graph bundles over K_4\e-free simple base. We also give a polynomial algorithm for recognizing Cartesian graph bundles over K_4\e-free simple base.