On a class of degenerate extremal graph problems
✍ Scribed by Ralph J. Faudree; Miklós Simonovits
- Book ID
- 110564389
- Publisher
- Springer-Verlag
- Year
- 1983
- Tongue
- English
- Weight
- 507 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0209-9683
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## Abstract We consider the family of graphs with a fixed number of vertices and edges. Among all these graphs, we are looking for those minimizing the sum of the square roots of the vertex degrees. We prove that there is a unique such graph, which consists of the largest possible complete subgraph
We consider extremal problems 'of Tur~ type' for r-uniform ordered hypergraphs, where multiple oriented edges are permitted up to multiplicity q. With any such '(r, q)-graph' G" we associate an r-linear form whose maximum over the standard (n -1)-simplex in R" is called the (graph-) density g(G ") o