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Hypergraphs with no odd cycle of given length

✍ Scribed by Ervin Győri; Nathan Lemons

Book ID
108120717
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
166 KB
Volume
34
Category
Article
ISSN
1571-0653

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## 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)__