New linear-time algorithms for edge-coloring planar graphs

Richard Cole, Łukasz Kowalik

Research output: Contribution to journalArticle

Abstract

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 O(n log n) time.

Original languageEnglish (US)
Pages (from-to)351-368
Number of pages18
JournalAlgorithmica (New York)
Volume50
Issue number3
DOIs
StatePublished - Feb 2008

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Edge Coloring
Coloring
Linear-time Algorithm
Planar graph
Color
Maximum Degree
Colouring
Linear Time
Efficient Algorithms
Graph in graph theory

Keywords

  • Algorithm
  • Edge-coloring
  • Linear-time
  • Planar graph

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality

Cite this

New linear-time algorithms for edge-coloring planar graphs. / Cole, Richard; Kowalik, Łukasz.

In: Algorithmica (New York), Vol. 50, No. 3, 02.2008, p. 351-368.

Research output: Contribution to journalArticle

Cole, Richard ; Kowalik, Łukasz. / New linear-time algorithms for edge-coloring planar graphs. In: Algorithmica (New York). 2008 ; Vol. 50, No. 3. pp. 351-368.
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