The k-in-a-path Problem for Claw-free Graphs

Jiri Fiala, Marcin Kaminski, Bernard Lidický & DaniëL Paulusma
Testing whether there is an induced path in a graph spanning $k$ given vertices is already \NP-complete in general graphs when $k=3$. We show how to solve this problem in polynomial time on claw-free graphs, when $k$ is not part of the input but an arbitrarily fixed integer.