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Planar Graphs Without Cycles of Length from 4 to 7 and Intersecting Triangles are DP-3-Colorable

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Abstract

DP-coloring (also known as correspondence coloring) as a generalization of list coloring was introduced recently by Dvořák and Postle. In this paper, we prove that planar graphs without cycles of length from 4 to 7 and intersecting triangles are DP-3-colorable and therefore 3-choosable. We use identification of vertices in the proof, and actually prove stronger statements that every pre-coloring of some short cycles can be extended to the whole graph.

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Acknowledgements

Research of Jian-Bo Lv was supported by NSFC (No.12161010) and Youth Science Foundation of Guangxi (No.2019JJB110007).

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  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin, 541000, People’s Republic of China

    Jian-Bo Lv

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  1. Jian-Bo Lv
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Correspondence to Jian-Bo Lv.

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Lv, JB. Planar Graphs Without Cycles of Length from 4 to 7 and Intersecting Triangles are DP-3-Colorable. Graphs and Combinatorics 38, 8 (2022). https://doi.org/10.1007/s00373-021-02407-5

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  • DOI: https://doi.org/10.1007/s00373-021-02407-5

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