Pathwidth of hyperbolic random graphs

Determine exact results for the pathwidth of the hyperbolic random graph model G_hyp(n, alpha) with alpha > 1/2, specifying how the pathwidth scales with n and alpha (with high probability), to enable direct application of pathwidth-based strategies such as the PW algorithm.

Background

The paper compares a separator-based strategy (STT) with a pathwidth-based strategy (PW) for the zero-visibility Cops and Robbers game. While PW relies on path decompositions, the authors note that for hyperbolic random graphs there are no exact pathwidth results available, which limits the direct use of PW in that setting.

Because separator and treewidth bounds are known for hyperbolic random graphs, the authors analyze the STT approach there; however, the absence of exact pathwidth results remains a gap that prevents analogous PW-based guarantees. Establishing the pathwidth would clarify the relationship between these approaches on hyperbolic random graphs.