On a graph colouring problem

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Abstract

A graph G = (V,E) is said to be k-emulsive if it admits an edge-colouring ψ : E → [k] = {1, 2, . . . , k} such that, for any vertex-colouring φ : V → [k] there exists an edge e = {x, y} such that φ(x) = φ(y) = ψ(e). We show, by construction, that the complete graph on (1 + o(1))k2vertices is k-emulsive. This settles a question raised by Cochand and Duchet. © 1999 Published by Elsevier Science B.V. All rights reserved.

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Cochand, M., & Károlyi, G. (1999). On a graph colouring problem. Discrete Mathematics, 194(1–3), 249–252. https://doi.org/10.1016/S0012-365X(98)00060-0

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