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A Grötzsch-Type Theorem for List Colourings with Impropriety One

Published online by Cambridge University Press:  01 September 1999

R. šKREKOVSKI
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia (e-mail: skreko@fmf.uni-lj.si)

Abstract

A graph G is m-choosable with impropriety d, or simply (m, d)*-choosable, if, for every list assignment L, where [mid ]L(v)[mid ][ges ]m for every vV(G), there exists an L-colouring of G such that each vertex of G has at most d neighbours coloured with the same colour as itself. We prove a Grötzsch-type theorem for list colourings with impropriety one, that is, the (3, 1)*-choosability for triangle-free planar graphs; in the proof the method of extending a precolouring of a 4- or 5-cycle is used.

Type
Research Article
Copyright
1999 Cambridge University Press

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