The k-in-a-path problem for claw-free graphs

TL;DR

This paper presents a polynomial-time solution for the k-in-a-path problem in claw-free graphs, which is NP-complete in general graphs for k=3, by fixing k as a constant.

Contribution

It introduces a polynomial-time algorithm for the k-in-a-path problem specifically in claw-free graphs with fixed k, extending the understanding of path problems in specialized graph classes.

Findings

Polynomial-time algorithm for fixed k in claw-free graphs

NP-completeness of the problem in general graphs for k=3

Advancement in graph path problem complexity analysis

Abstract

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.