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On induced colourful paths in triangle-free graphs

Babu, Jasine and Basavaraju, Manu and Chandran, L Sunil and Francis, Mathew C (2019) On induced colourful paths in triangle-free graphs. In: DISCRETE APPLIED MATHEMATICS, 255 . pp. 109-116.

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Official URL: https://doi.org/10.1016/j.dam.2018.08.004


Given 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 chi(G) vertices. We explore a conjecture that states that every properly coloured triangle free graph G contains an induced colourful path on chi(G) vertices and prove its correctness when the girth of G is at least chi(G). Recent work on this conjecture by Gyarfas and Sarkozy, and Scott and Seymour has shown the existence of a function f such that if chi(G) >= f (k), then an induced colourful path on k vertices is guaranteed to exist in any properly coloured triangle-free graph G. (C) 2018 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Additional Information: copyright for this article belongs to DISCRETE APPLIED MATHEMATICS
Keywords: Induced path; Colourful path; Triangle-free graph
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 15 May 2019 13:19
Last Modified: 15 May 2019 13:19
URI: http://eprints.iisc.ac.in/id/eprint/62429

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