The work is devoted to the calculation of asymptotic value of the choice number of the complete r-partite graph K m \* r = K m,. ..,m with equal part size m. We obtained the asymptotics in the case ln r = o(ln m). The proof generalizes the classical result of A.L. Rubin for the case r = 2.
On a generalization of Minkowski's convex body theorem
✍ Scribed by Béla Uhrin
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 791 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract In this paper, we obtain an asymptotic generalization of Turán's theorem. We prove that if all the non‐trivial eigenvalues of a __d__‐regular graph __G__ on __n__ vertices are sufficiently small, then the largest __K__~__t__~‐free subgraph of __G__ contains approximately (__t__ − 2)/(__
Let 9 be the polyhedron given by 9 = {x E R": Nx=O, a~x~b}, where N is a totally unimodular matrix and a and 6 are any integral vectors. For x E R" let (x)' denote the vector obtained from x by changing all its negative components to zeros. Let x1, . . . , xp be the integral points in 9 and let 9+ b
The following theorem is lproved. If the sets VI, . . . , Vn+, CR" and a E fly:: conv Vi, then there exist elements ui E Vi (i = 1, . . . , n + 1) such that a E conv{o,, . . . , un+J. Thii is a generalization of Carathtidory's theorem. By applying this and similar results some open questions are ans