Proof of the Erdős matching conjecture in a new range

Autor: Peter Frankl
Rok vydání: 2017
Předmět:
Zdroj: Israel Journal of Mathematics. 222:421-430
ISSN: 1565-8511
0021-2172
DOI: 10.1007/s11856-017-1595-7
Popis: Let s > k ≧ 2 be integers. It is shown that there is a positive real e = e(k) such that for all integers n satisfying (s + 1)k ≦ n < (s + 1)(k + e) every k-graph on n vertices with no more than s pairwise disjoint edges has at most $$\left( {\begin{array}{*{20}{c}} {\left( {s + 1} \right)k - 1} \\ k \end{array}} \right)$$ edges in total. This proves part of an old conjecture of Erdős.
Databáze: OpenAIRE