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arXiv · 1301.6898

Square Property, Equitable Partitions, and Product-like Graphs

Marc Hellmuth·Lydia Ostermeier·Peter F. Stadler
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Abstract

Equivalence relations on the edge set of a graph $G$ that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way induce equitable partitions on the vertex set of $G$, which in turn give rise to quotient graphs that can have a rich product structure even if $G$ itself is prime.

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Marc Hellmuth, Lydia Ostermeier, Peter F. Stadler. 2013-01-29. Square Property, Equitable Partitions, and Product-like Graphs. https://doi.org/10.1016/j.disc.2013.12.012

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