The Relaxed Square Property
Discrete Mathematics
2014-07-14 v1 Combinatorics
Abstract
Graph products are characterized by the existence of non-trivial equivalence relations on the edge set of a graph that satisfy a so-called square property. We investigate here a generalization, termed RSP-relations. The class of graphs with non-trivial RSP-relations in particular includes graph bundles. Furthermore, RSP-relations are intimately related with covering graph constructions. For K_23-free graphs finest RSP-relations can be computed in polynomial-time. In general, however, they are not unique and their number may even grow exponentially. They behave well for graph products, however, in sense that a finest RSP-relations can be obtained easily from finest RSP-relations on the prime factors.
Cite
@article{arxiv.1407.3164,
title = {The Relaxed Square Property},
author = {Marc Hellmuth and Tilen Marc and Lydia Ostermeier and Peter F. Stadler},
journal= {arXiv preprint arXiv:1407.3164},
year = {2014}
}