## 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)__
✦ LIBER ✦
Color-critical graphs and hypergraphs with few edges and no short cycles
✍ Scribed by H.L. Abbott; D.R. Hare; B. Zhou
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 378 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
We give constructions of color-critical graphs and hypergraphs with no cycles of length 5 or shorter and with relatively few edges.
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## Abstract Sufficient degree conditions for the existence of properly edge‐colored cycles and paths in edge‐colored graphs, multigraphs and random graphs are investigated. In particular, we prove that an edge‐colored multigraph of order __n__ on at least three colors and with minimum colored degre