Proof of the Erdős matching conjecture in a new range
Autor: | Peter Frankl |
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Rok vydání: | 2017 |
Předmět: |
Discrete mathematics
Conjecture Matching (graph theory) General Mathematics 010102 general mathematics 0102 computer and information sciences Disjoint sets 01 natural sciences Erdős–Gyárfás conjecture Collatz conjecture Combinatorics 010201 computation theory & mathematics Beal's conjecture 0101 mathematics Erdős–Straus conjecture Mathematics Range (computer programming) |
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 |
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