Log-concavity of all well-covered forests

Determine whether every well-covered forest has a log-concave independence polynomial at every internal coefficient index.

Background

The paper proves strict log-concavity for well-covered forests whose matching number is at least the eventual threshold established for large forests. This condition controls the nonisolated part and does not follow merely from having large total order when isolated vertices are present.

The unresolved problem asks whether the conclusion holds without the matching-number threshold. The authors note that the forest barrier conjecture together with their corona-transfer theorem would yield the stronger strict conclusion at all internal indices, including for well-covered forests with isolated components.