Finding an induced path that is not a shortest path

TL;DR

This paper presents a polynomial-time algorithm to determine whether a graph contains an induced path between two vertices that is longer than the shortest possible induced path.

Contribution

The paper introduces the first efficient algorithm for identifying induced paths longer than the shortest between two vertices in a graph.

Findings

Algorithm runs in polynomial time

Decides existence of longer induced paths efficiently

Advances understanding of induced path structures

Abstract

We give a polynomial-time algorithm that, with input a graph $G$ and two vertices $u,v$ of $G$, decides whether there is an induced $uv$-path that is longer than the shortest $uv$-path.