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Graphs of Large Girth with Prescribed Partial Circular Colourings

✍ Scribed by Zhishi Pan; Xuding Zhu


Book ID
106047538
Publisher
Springer Japan
Year
2005
Tongue
English
Weight
399 KB
Volume
21
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES


Total Colourings of Planar Graphs with L
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It is proved that if G is a planar graph with total (vertex-edge) chromatic number Ο‡ , maximum degree and girth g, then Ο‡ = + 1 if β‰₯ 5 and g β‰₯ 5, or β‰₯ 4 and g β‰₯ 6, or β‰₯ 3 and g β‰₯ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.

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It was proved by Hell and Zhu that, if G is a series-parallel graph of girth at least 2 (3k -1)/2 , then Ο‡ c (G) ≀ 4k/(2k -1). In this article, we prove that the girth requirement is sharp, i.e., for any k β‰₯ 2, there is a series-parallel graph G of girth 2 (3k -1)/2 -1 such that Ο‡ c (G) > 4k/(2k -1)

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