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Total Colourings of Planar Graphs with Large Girth

✍ Scribed by O.V. Borodin; A.V. Kostochka; D.R. Woodall

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 96 KB
Volume: 19
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1997.0152

No coin nor oath required. For personal study only.

✦ Synopsis

It is proved that if G is a planar graph with total (vertex-edge) chromatic number χ , maximum degree and girth g, then χ = + 1 if ≥ 5 and g ≥ 5, or ≥ 4 and g ≥ 6, or ≥ 3 and g ≥ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.

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