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Brillouin zones and the geometry of numbers

โœ Scribed by M. M. Skriganov


Publisher
Springer US
Year
1987
Tongue
English
Weight
940 KB
Volume
36
Category
Article
ISSN
1573-8795

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Graphs on the Torus and Geometry of Numb
โœ A. Schrijver ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 424 KB

We show that if \(G\) is a graph embedded on the torus \(S\) and each nonnullhomotopic closed curve on \(S\) intersects \(G\) at least \(r\) times, then \(G\) contains at least \(\left\lfloor\frac{3}{4} r\right\rfloor\) pairwise disjoint nonnullhomotopic circuits. The factor \(\frac{3}{4}\) is best