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DP-4-coloring of planar graphs with some restrictions on cycles
Discrete Mathematics ( IF 0.8 ) Pub Date : 2021-08-02 , DOI: 10.1016/j.disc.2021.112568
Rui Li 1 , Tao Wang 1
Affiliation  

DP-coloring was introduced by Dvořák and Postle as a generalization of list coloring. It was originally used to solve a longstanding conjecture by Borodin, stating that every planar graph without cycles of lengths 4 to 8 is 3-choosable. In this paper, we give three sufficient conditions for a planar graph to be DP-4-colorable. Actually all the results (Theorem 1.3, Theorem 1.4, Theorem 1.7) are stated in the “color extendability” form, and uniformly proved by vertex identification and discharging method.



中文翻译:

平面图的 DP-4 着色,对循环有一些限制

Dvořák 和 Postle 引入了 DP 着色,作为列表着色的概括。它最初用于解决 Borodin 的一个长期猜想,指出每个没有长度为 4 到 8 的圈的平面图都是 3-choosable 的。在本文中,我们给出了平面图是 DP-4 可着色的三个充分条件。实际上所有的结果(定理1.3、定理1.4、定理1.7)都以“颜色可延展性”的形式表述,并用顶点识别和放电方法统一证明。

更新日期:2021-08-02
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