Rainbow matchings in k ‐partite hypergraphs
@article{Kiselev2020RainbowMI, title={Rainbow matchings in k ‐partite hypergraphs}, author={S. G. Kiselev and Andrey B. Kupavskii}, journal={Bulletin of the London Mathematical Society}, year={2020}, volume={53} }
In this paper, we prove a conjecture of Aharoni and Howard on the existence of rainbow (transversal) matchings in sufficiently large families F1,…,Fs of tuples in {1,…,n}k , provided s⩾470 .
6 Citations
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References
SHOWING 1-10 OF 21 REFERENCES
Proof of the Erdős matching conjecture in a new range
- Mathematics
- 2017
AbstractLet s > k ≧ 2 be integers. It is shown that there is a positive real ε = ε(k) such that for all integers n satisfying (s + 1)k ≦ n < (s + 1)(k + ε) every k-graph on n vertices with no more…
The Erd\H{o}s Matching Conjecture and concentration inequalities.
- Mathematics
- 2018
More than 50 years ago, Erd\H os asked the following question: what is the maximum size of a family $\mathcal F$ of $k$-element subsets of an $n$-element set if it has no $s+1$ pairwise disjoint…
The Size of a Hypergraph and its Matching Number
- MathematicsCombinatorics, Probability and Computing
- 2012
This paper verifies the conjecture that for any $t < \frac{n}{3k^2}$, every k-uniform hypergraph on n vertices without t disjoint edges has at most max $binom{kt-1}{k}-\binom-n-t-t+1-k$ edges.
A Rainbow r-Partite Version of the Erdős–Ko–Rado Theorem
- MathematicsCombinatorics, Probability and Computing
- 2017
Let [n] r be the complete r-partite hypergraph with vertex classes of size n. It is an easy exercise to show that every set of more than (k−1)n r−1 edges in [n] r contains a matching of size k. We…
Explicit construction of linear sized tolerant networks
- Mathematics, Computer ScienceDiscret. Math.
- 1988
Beyond the Erd\H{o}s Matching Conjecture
- Mathematics
- 2019
A generalization of the Erdős-Ko-Rado theorem is proved, which states that for $n> s^2k$ the largest family with property U(s,s(k-1)+1)$ is the star and is in particular intersecting.
On Rainbow Matchings for Hypergraphs
- MathematicsSIAM J. Discret. Math.
- 2018
It is shown that for sufficiently large $n$ with $\sum_{i=1}^t k_i\leq n(1-(4k\ln n/n)^{1/k}) $, the bound is tight.
Simple juntas for shifted families
- MathematicsArXiv
- 2019
Very general approximation by juntas results for shifted families with explicit (and essentially linear) dependency on the input parameters are presented.
A PROBLEM ON INDEPENDENT r-TUPLES
- Mathematics
- 1965
then G(n ; l) contains k independent edges . It is easy to see that the above result is best possible since the complete graph of 2k-1 vertices and the graph of vertices x1, . . ., xk-1 ; Yl, • • •,…
Concentration Inequalities and Martingale Inequalities: A Survey
- Mathematics, EconomicsInternet Math.
- 2006
We examine a number of generalized and extended versions of concentration inequalities and martingale inequalities. These inequalities are effective for analyzing processes with quite general…