Babu, J.Basavaraju, M.Chandran, L.S.Francis, M.C.2020-03-312020-03-312019Discrete Applied Mathematics, 2019, Vol.255, , pp.109-116https://idr.nitk.ac.in/handle/123456789/12360Given a graph G=(V,E) whose vertices have been properly coloured, we say that a path in G is colourful if no two vertices in the path have the same colour. It is a corollary of the Gallai Roy Vitaver Theorem that every properly coloured graph contains a colourful path on ?(G) vertices. We explore a conjecture that states that every properly coloured triangle-free graph G contains an induced colourful path on ?(G) vertices and prove its correctness when the girth of G is at least ?(G). Recent work on this conjecture by Gy rf s and S rk zy, and Scott and Seymour has shown the existence of a function f such that if ?(G)?f(k), then an induced colourful path on k vertices is guaranteed to exist in any properly coloured triangle-free graph G. 2018 Elsevier B.V.Article