Reconfiguring Independent Sets on Interval Graphs

We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size \(k\) are reconfigurable in an \(n\)-vertex interval graph, then there is a reconfiguration sequence of length \(\mathcal{O}(k\cdot n^2)\). We also provide a construction in which the shortest reconfiguration sequence is of length \(\Omega(k^2\cdot n)\). As a counterpart to these results, we also establish that \(\textsf{Independent Set Reconfiguration}\) is PSPACE-hard on incomparability graphs, of which interval graphs are a special case.