New Linear-Time Algorithms for Edge-Coloring Planar Graphs

We show efficient algorithms for edge-coloring planar graphs. Our main result is a linear-time algorithm for coloring planar graphs with maximum degree with max{, 9} colors. Thus the coloring is optimal for graphs with maximum degree 9. Moreover for = 4, 5, 6 we give linear-time algorithms that use + 2 colors. These results improve over the algorithms of Chrobak and Yung [1] and of Chrobak and Nishizeki [2] which color planar graphs using max{, 19} colors in linear time or using max{, 9} colors in O(n log n) time. Keywords. Edge-coloring, linear-time, algorithm, planar graph

• Type: Journal
• Year: 2008
• Where: ALGORITHMICA
• Authors: Richard Cole, Lukasz Kowalik
• Keywords: Algorithm, ALGORITHMICA 2008, Maximum Degree, Planar Graphs