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Discussiones Mathematicae Graph Theory 22(2) (2002) 293-303
DOI: https://doi.org/10.7151/dmgt.1176

ON THE STRUCTURAL RESULT ON NORMAL PLANE MAPS

Tomás Madaras and Andrea Marcinová

Department of Geometry and Algebra
P.J. Safárik University
Jesenná 5, 041 54 Košice, Slovak Republic

Abstract

We prove the structural result on normal plane maps, which applies to the vertex distance colouring of plane maps. The vertex distance-t chromatic number of a plane graph G with maximum degree Δ(G) ≤ D, D ≥ 12 is proved to be upper bounded by 6+[(2D+12)/(D−2)] ((D−1)^(t−1)−1). This improves a recent bound 6+[(3D+3)/(D−2)]((D−1)^t−1−1), D ≥ 8 by Jendrol' and Skupień, and the upper bound for distance-2 chromatic number.

Keywords: plane map, distance colouring.

2000 Mathematics Subject Classification: 05C10.

References

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Received 24 April 2001
Revised 23 March 2002