, Volume 50, Issue 3, pp 351-368

First online:

New Linear-Time Algorithms for Edge-Coloring Planar Graphs

  • Richard ColeAffiliated withComputer Science Department, New York University
  • , Łukasz KowalikAffiliated withInstitute of Informatics, Warsaw University Email author 

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We show efficient algorithms for edge-coloring planar graphs. Our main result is a linear-time algorithm for coloring planar graphs with maximum degree Δ with max {Δ,9} colors. Thus the coloring is optimal for graphs with maximum degree Δ≥9. Moreover for Δ=4,5,6 we give linear-time algorithms that use Δ+2 colors. These results improve over the algorithms of Chrobak and Yung (J. Algorithms 10:35–51, 1989) and of Chrobak and Nishizeki (J. Algorithms 11:102–116, 1990) which color planar graphs using max {Δ,19} colors in linear time or using max {Δ,9} colors in \(\mathcal{O}(n\log n)\) time.


Edge-coloring Linear-time Algorithm Planar graph