Constructive extendability in C-expanders

Determine whether there exists a constructive (algorithmic) version of the extendability embedding method for general C-expanders that enables building structures such as the linking structure in polynomial time while maintaining (D,m)-extendability.

Background

The extendability method used to embed long paths and linking structures into expanders is based on a non-constructive argument. While constructive variants exist for robust expanders (hence for (n,d,λ)-graphs), a general algorithmic version for C-expanders is not known.

This impacts the algorithmic extraction of Hamilton cycles in general expanders; the authors circumvent it for spectral expanders via known constructive tools, leaving the general constructive question unresolved.