Coloring Non-uniform Hypergraphs Without Short Cycles
✍ Scribed by Dmitry A. Shabanov
- Book ID
- 120788868
- Publisher
- Springer Japan
- Year
- 2013
- Tongue
- English
- Weight
- 196 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0911-0119
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📜 SIMILAR VOLUMES
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
## Abstract We give constructions of color‐critical graphs and hypergraphs with no short cycles and with relatively few edges. In particular, we show that, for each __n__ ≧ 3, the smallest number of edges in a 3‐critical triangle‐free __n__‐graph (hypergraph) with __m__ vertices is __m__ + __o(m)__