Four colouring the vertices of the triangulation of a polygon containing a hole

Authors:
Graham M. Seed;Douglas E. R. Clark;Raffaella Ocone;Xiaoyan Y. Yang
Affiliations:
School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, Scotland;School of Mathematical and Computing Sciences, Heriot-Watt University, Edinburgh, Scotland;School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, Scotland;School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, Scotland
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Year:
2003

Citing 2
Cited 0

Computational geometry in C

Computational geometry in C
The four-colour theorem

Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday

Quantified Score

Hi-index	0.00

Visualization

Abstract

A simple linear-time algorithm is presented for four-colouring the vertices of a triangulation of a polygon containing a single hole. The algorithm consists of reducing a triangulation by the removal of both polygon and hole ear vertices, if any, followed by the removal of colour-isolated vertices until a 3-coloured tessellation remains. The triangulation is then re-built, using at most four colours. The paper concludes by recognising the similarity between the colouring of triangulations of polygons containing a hole and the colouring of bipartite and permutation graphs.