A note on embedding graphs without short cycles
✍ Scribed by Agnieszka Görlich; Monika Pilśniak; Mariusz Woźniak; Irmina A. Zioło
- Book ID
- 108113405
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 169 KB
- Volume
- 286
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
In this note we prove that every 2-connected graph of order n with no repeated cycle lengths has at most n + 2(n -2) -1 edges and we show this result is best possible with the correct order of magnitude on √ n. The 2connected case is also used to give a quick proof of Lai's result on the general cas
## 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.
It is shown that there is a constant \(c\) such that if \(G\) is a graph embedded in a surface of genus \(g\) (either orientable or non-orientable) and the length of a shortest non-bounding cycle of \(G\) is at least \(c \log (g+1)\), then \(G\) is six-colorable. A similar result holds for three- an