Fast 3-Coloring Triangle-Free Planar Graphs

We show the first o(n2 ) algorithm for coloring vertices of trianglefree planar graphs using three colors. The time complexity of the algorithm is O(n log n). Our approach can be also used to design O(n polylog n)-time algorithms for two other similar coloring problems. A remarkable ingredient of our algorithm is the data structure processing short path queries introduced recently in [9]. In this paper we show how to adapt it to the fully dynamic environment where edge insertions and deletions are allowed.

• Type: Conference
• Year: 2004
• Where: ESA
• Authors: Lukasz Kowalik
• Keywords: Algorithm, ESA 2004, Similar Coloring Problems, Trianglefree Planar Graphs