Two linear-time algorithms for five-coloring a planar graph

Authors:
David W. Matula;Yossi Shiloach;Robert E. Tarjan
Affiliations:
-;-;-
Venue:
Two linear-time algorithms for five-coloring a planar graph
Year:
1980

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Abstract

A "sequential processing" algorithm using bicolor interchange that five-colors an n vertex planar graph in $O(n^2)$ time was given by Matula, Marble, and Isaacson [1972]. Lipton and Miller used a "batch processing" algorithm with bicolor interchange for the same problem and achieved an improved O(n log n) time bound [1978]. In this paper we use graph contraction arguments instead of bicolor interchange and improve both the sequential processing and batch processing methods to obtain five-coloring algorithms that operate in O(n) time.