List Improper Colourings of Planar Graphs

  • Authors:

  • R. Škrekovski

  • Affiliations:

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

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 1999

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Abstract

A graph G is m-choosable with impropriety d, or simply (m, d)*-choosable, if for every list assignment L, where ∣L(v)∣≥m for every v∈V(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.