The extremal graph problem of the icosahedron
✍ Scribed by Simonovits Miklós
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 528 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0095-8956
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📜 SIMILAR VOLUMES
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
Let r be a 3-polytopal graph such that every face of r is convex. We prove that if the set of proper convex subgraphs of r is equal to the set of proper convex subgraphs of the dodecahedron (resp. icosahedron), then F is isomorphic to the dodecahedron (resp. icosahedron).
## Abstract For __n__ sufficiently large the order of a smallest balanced extension of a graph of order __n__ is, in the worst case, ⌊(__n__ + 3)^2^/8⌋. © 1993 John Wiley & Sons, Inc.
concerning the well-known diophantine problem of Frobenius was given an exact solution for linear forms with the set of coefficients of density 1 2 (or more). In the present paper, we advance this up to the density 1 3 .