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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Abstract

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
Publication:	DISCRETE APPLIED MATHEMATICS
Publisher:	ELSEVIER SCIENCE BV
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
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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