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Coarse Differentiation and Multi-flows in Planar Graphs

✍ Scribed by James R. Lee; Prasad Raghavendra

Publisher
Springer
Year
2009
Tongue
English
Weight
490 KB
Volume
43
Category
Article
ISSN
0179-5376

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## Abstract We prove that every oriented planar graph admits a homomorphism to the Paley tournament __P__~271~ and hence that every oriented planar graph has an antisymmetric flow number and a strong oriented chromatic number of at most 271. Β© 2006 Wiley Periodicals, Inc. J Graph Theory 52: 200–210

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NeΓ„ setΓ„ ril and Raspaud (Ann. Inst. Fourier 49 (3) (1999) 1037-1056) deΓΏned antisymmetric ow, which is a variant of nowhere zero ow, and a dual notion to strong oriented coloring. We give an upper bound on the number of colors needed for a strong oriented coloring of a planar graph, and hereby we ΓΏ

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