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Acta Mathematica Vietnamica

, Volume 44, Issue 2, pp 493–500 | Cite as

On Chromatic Numbers of Two Extensions of Planar Graphs

  • Khosro TajbakhshEmail author
Article
  • 33 Downloads

Abstract

In this paper, the acyclic chromatic and the circular list chromatic numbers of a simple H-minor free graph G is considered, where H ∈{K5,K3,3}. It is proved that the acyclic chromatic number (resp. the circular list chromatic number) of a simple H-minor free graph G where H ∈{K5,K3,3} is at most 5 (resp. at most 8) and we conclude that G is star 20-colorable. These results generalize the same known results on planar graphs. Moreover, some upper bounds for the coloring numbers of H-minor free graphs for H ∈{K5,K3,3,Kr,s} and r ≤ 2 are obtained. These results generalize some known results and give some new results on group choice number, group chromatic number, and the choice number of the mentioned graphs with much shorter proofs.

Keywords

Acyclic coloring Star coloring Circular choosability Coloring number Planar graphs 

Mathematics Subject Classification (2010)

05C15 

Notes

Acknowledgements

The author wishes to thank Dr. G. R. Omidi for the useful comments and suggestions regarding the manuscript. I also would like to thank the anonymous referee for his/her useful comments.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Pure Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran

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