Generalization of the Gale–Ryser Theorem
✍ Scribed by Anatol N. Kirillov
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 126 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0195-6698
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## 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)/(__
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.
Let K = {Itl,. . . , k,} and L ={I1,. . . , Z,} be two sets of non-negative integers and assume ki > l j for every i , j . Let T be an L-intersecting family of subsets of a set of n elements. Assume the size of every set in T is a number from K. We conjecture that 1 ' f l 5 (: ). We prove that our c