Partial Online List Coloring of Graphs |
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Authors: | Tsai‐Lien Wong Xuding Zhu |
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Affiliation: | 1. DEPARTMENT OF APPLIED MATHEMATICS, NATIONAL SUN YAT‐SEN UNIVERSITY, , KAOHSIUNG 80424, TAIWAN;2. DEPARTMENT OF MATHEMATICS, ZHEJIANG NORMAL UNIVERSITY, , JINHUA, ZHEJIANG, CHINA, 321004 |
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Abstract: | For a graph G, let 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 , then . In this article, we consider the online version of this conjecture. Let 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 then . This article generalizes some results concerning partial list coloring to online partial list coloring. We prove that for any positive integers , . As a consequence, if s is a multiple of t, then . We also prove that if G is online s‐choosable and , then and for any , . |
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Keywords: | choice number online choice number partial list coloring online partial list coloring |
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