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Fractional total colourings of graphs of high girth

✍ Scribed by Tomáš Kaiser; Andrew King; Daniel Králʼ


Book ID
113698875
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
273 KB
Volume
101
Category
Article
ISSN
0095-8956

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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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