Preprint in the OpenAI Math release
The complexity of identifying a graph by Weisfeiler–Leman refinement
OpenAI
Abstract
We prove that deciding whether Weisfeiler–Leman refinement of an input dimension identifies a given graph is EXPTIME-complete. The input is a nonempty finite simple uncolored graph in adjacency-matrix form and a positive binary-encoded dimension. Identification quantifies over every comparison graph.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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