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Planar Graphs Without 4-Cycles Adjacent to Triangles are DP-4-Colorable

  • Seog-Jin Kim
  • Xiaowei YuEmail author
Original Paper
  • 3 Downloads

Abstract

DP-coloring (also known as correspondence coloring) of a simple graph is a generalization of list coloring. It is known that planar graphs without 4-cycles adjacent to triangles are 4-choosable, and planar graphs without 4-cycles are DP-4-colorable. In this paper, we show that planar graphs without 4-cycles adjacent to triangles are DP-4-colorable, which implies the two results above.

Keywords

Coloring List-coloring DP-coloring Signed graph 

Notes

Acknowledgements

This paper was written as part of Konkuk University’s research support program for its faculty on sabbatical leave in 2018 (S.-J. Kim). The second author is supported by Science Foundation of Jiangsu Normal University (18XLRX020), the National Natural Science Foundation of China (11871311) and the Shandong Provincial Natural Science Foundation of China (ZR2018BA010, ZR2018MA001).

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics EducationKonkuk UniversitySeoulKorea
  2. 2.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouPeople’s Republic of China

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