Partial Online List Coloring of Graphs

Authors


  • Contract grant sponsor: National Center for Theoretical Sciences (to T.-L. W.); Contract grant number: 99-2115-M-110-001-MY3; Contract grant sponsor: GraTel (to T.-L. W.); Contract grant number: ANR-09-BLAN-0373-01; Contract grant sponsor: NSFC (to X. Z.); Contract grant number: 11171730; Contract grant sponsor: ZJNSF (to X. Z.); Contract grant number: Z6110786.

Abstract

For a graph G, let math formula be the maximum number of vertices of G that can be colored whenever each vertex of G is given t permissible colors. Albertson, Grossman, and Haas conjectured that if G is s-choosable and math formula, then math formula. In this article, we consider the online version of this conjecture. Let math formula be the maximum number of vertices of G that can be colored online whenever each vertex of G is given t permissible colors online. An analog of the above conjecture is the following: if G is online s-choosable and math formula then math formula. This article generalizes some results concerning partial list coloring to online partial list coloring. We prove that for any positive integers math formula, math formula. As a consequence, if s is a multiple of t, then math formula. We also prove that if G is online s-choosable and math formula, then math formula and for any math formula, math formula.

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