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Finite fields and the 1-chromatic number of orientable surfaces

✍ Scribed by Vladimir P. Korzhik

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
98 KB
Volume
63
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

The 1‐chromatic number Ο‡~1~(S~p~) of the orientable surface S~p~ of genus p is the maximum chromatic number of all graphs which can be drawn on the surface so that each edge is crossed by no more than one other edge. We show that if there exists a finite field of order 4__m__+1, mβ‰₯3, then 8__m__+2≀χ~1~(S)≀8__m__+3, where 8__m__+3 is Ringel's upper bound on Ο‡~1~(S). Β© 2009 Wiley Periodicals, Inc. J Graph Theory 63: 179–184, 2010

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