It is shown that any 4-chromatic graph on n vertices contains an odd cycle of length smaller than √ 8n.
Small odd cycles in 4-chromatic graphs
✍ Scribed by Tao Jiang
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 50 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0364-9024
- DOI
- 10.1002/jgt.1006
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✦ Synopsis
Abstract
It is shown that every 4‐chromatic graph on n vertices contains an odd cycle of length less than $2\sqrt {n},+3$. This improves the previous bound given by Nilli [J Graph Theory 3 (1999), 145–147]. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 115–117, 2001
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