Short cycles of Poncelet’s conics
✍ Scribed by Boris Mirman
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 679 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
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📜 SIMILAR VOLUMES
## Abstract Let __G__ be a toroidal graph without cycles of a fixed length __k__, and χ~__l__~(__G__) the list chromatic number of __G__. We establish tight upper bounds of χ~__l__~(__G__) for the following values of __k__: © 2009 Wiley Periodicals, Inc. J Graph Theory 65: 1–15, 2010.
In this paper we prove: (i) If a graph \(G\) has a nowhere-zero 6 -llow \(\phi\) such that \(\left|E_{\text {odd }}(\phi)\right| \geqslant \frac{2}{3}|E(G)|\), then \(G\) has a cycle cover in which the sum of the lengths of the cycles in the cycle cover is at most \(\frac{44}{27}|E(G)|\), where \(E_