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List Improper Colourings of Planar Graphs

Published online by Cambridge University Press:  01 May 1999

Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia (e-mail: riste.skrekovski@FMF.Uni-Lj.Si)


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 show that every planar graph is (3, 2)*-choosable and every outerplanar graph is (2, 2)*-choosable. We also propose some interesting problems about this colouring.

Research Article
1999 Cambridge University Press

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