Polynomial-time solvability of Fast-Strategy on unit interval graphs

Determine whether Fast-Strategy can be decided in polynomial time on unit interval graphs, and more generally identify additional graph classes for which Fast-Strategy is polynomial-time solvable.

Background

Beyond the classes handled in the paper (trees and cographs), the authors suggest exploring other structured graph families where Fast-Strategy might admit efficient algorithms. Unit interval graphs are highlighted as promising candidates, potentially allowing adaptation of the arena-based methods developed for trees.

A positive result would extend the tractable frontier of Fast-Strategy and could reveal structural properties enabling efficient strategies and analyses.