Combinatorics Probability Computing· 2012Q1
The Size of a Hypergraph and its Matching Number
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- Q1SCImago
- 2012year
Short summary
Erdős's hypergraph conjecture is proven for $t < n/(3k^2)$, improving the prior range of $t = O(n/k^3)$.
AI-generated from the title and abstract; the full text is not read.
Key points
- The paper proves Erdős's conjecture for $t < n/(3k^2)$.
- This extends the previously known range of $t = O(n/k^3)$ for the conjecture.
- The conjecture relates to the maximum number of edges in a k-uniform hypergraph without t disjoint edges.
AI-generated from the title and abstract; the full text is not read.
Abstract
More than forty years ago, Erdős conjectured that for any $t \leq \frac{n}{k}$ , every k -uniform hypergraph on n vertices without t disjoint edges has at most max ${\binom{kt-1}{k}, \binom{n}{k}-\binom{n-t+1}{k}\}$ edges. Although this appears to be a basic instance of the hypergraph Turán problem (with a t -edge matching as the excluded hypergraph), progress on this question has remained elusive. In this paper, we verify this conjecture for all $t < \frac{n}{3k^2}$ . This improves upon the best previously known range $t = O\bigl(\frac{n}{k^3}\bigr)$ , which dates back to the 1970s.
The authors' abstract, as published at the source. Combinatorics Probability Computing, 2012 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics