Journal of Graph Algorithms and Applications
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Constructing Hard Examples for Graph Isomorphism
Vol. 23, no. 2, pp. 293-316, 2019. Regular paper.
Abstract We describe a method for generating graphs that provide difficult examples for practical Graph Isomorphism testers. We first give the theoretical construction, showing that we can have a family of graphs without any non-trivial automorphisms which also have high Weisfeiler-Leman dimension. The construction is based on properties of random 3XOR-formulas. We describe how to convert such a formula into a graph which has the desired properties with high probability. We validate the method by experimental implementations. We construct random formulas and validate them with a SAT solver to filter through suitable ones, and then convert them into graphs. Experimental results demonstrate that the resulting graphs do provide hard examples that match the hardest known benchmarks for graph isomorphism.
Submitted: September 2018.
Reviewed: January 2019.
Revised: March 2019.
Accepted: March 2019.
Final: April 2019.
Published: April 2019.
Communicated by Giuseppe Liotta