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      3-choosable planar graphs with some precolored vertices and no \(5^{-}\)-cycles normally adjacent to \(8^{-}\)-cycles

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          Abstract

          DP-coloring was introduced by Dvo\v{r}\'{a}k and Postle [J. Combin. Theory Ser. B 129 (2018) 38--54] as a generalization of list coloring. They used a "weak" version of DP-coloring to solve a longstanding conjecture by Borodin, stating that every planar graph without cycles of length \(4\) to \(8\) is \(3\)-choosable. Liu and Li improved the result by showing that every planar graph without adjacent cycles of length at most \(8\) is \(3\)-choosable. In this paper, it is showed that every planar graph without \(5^{-}\)-cycles normally adjacent to \(8^{-}\)-cycles is \(3\)-choosable. Actually, all these three papers give more stronger results by stating them in the form of "weakly" DP-\(3\)-coloring and color extension.

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          Most cited references 8

          • Record: found
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          Every Planar Graph Is 5-Choosable

           C. Thomassen (1994)
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            • Record: found
            • Abstract: not found
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            3-List-Coloring Planar Graphs of Girth 5

             C. Thomassen (1995)
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              • Record: found
              • Abstract: not found
              • Article: not found

              Colorings of plane graphs: A survey

               O.V Borodin (2013)
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                Author and article information

                Journal
                13 August 2019
                Article
                1908.04902

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                05C15
                9 pages, 2 figures
                math.CO cs.DM

                Combinatorics, Discrete mathematics & Graph theory

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