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pro vyhledávání: '"Delcourt"'
A family of $r$ distinct sets $\{A_1,\ldots, A_r\}$ is an $r$-sunflower if for all $1 \leqslant i < j \leqslant r$ and $1 \leqslant i' < j' \leqslant r$, we have $A_i \cap A_j = A_{i'} \cap A_{j'}$. Erd\H{o}s and Rado conjectured in 1960 that every f
Externí odkaz:
http://arxiv.org/abs/2408.04165
Publikováno v:
Clinical Interventions in Aging, Vol Volume 14, Pp 1471-1480 (2019)
Suzanne Cosh,1 Catherine Helmer,2 Cecile Delcourt,2 Tamara G Robins,3 Phillip J Tully41School of Psychology, University of New England, Armidale, NSW 2351, Australia; 2Bordeaux Population Health Research Center, University Bordeaux, Inserm, Team LEHA
Externí odkaz:
https://doaj.org/article/8b4e122facbb498d82c49748de529245
We prove that if $p \geq n^{-(q-6)/2}$, then asymptotically almost surely the binomial random $q$-uniform hypergraph $G^{(q)}(n,p)$ contains an $(n,q,2)$-Steiner system, provided $n$ satisfies the necessary divisibility conditions.
Comment: 17 p
Comment: 17 p
Externí odkaz:
http://arxiv.org/abs/2402.17858
We prove that if $p\ge n^{-\frac{1}{3}+\beta}$ for some $\beta > 0$, then asymptotically almost surely the binomial random graph $G(n,p)$ has a $K_3$-packing containing all but at most $n + O(1)$ edges. Similarly, we prove that if $d \ge n^{\frac{2}{
Externí odkaz:
http://arxiv.org/abs/2402.17857
Autor:
Delcourt, Michelle, Postle, Luke
We prove the High Girth Existence Conjecture - the common generalization of the Existence Conjecture for Combinatorial Designs originating from the 1800s and Erd\H{o}s' Conjecture from 1973 on the Existence of High Girth Steiner Triple Systems.
Externí odkaz:
http://arxiv.org/abs/2402.17856
Autor:
Delcourt, Michelle, Postle, Luke
The study of combinatorial designs has a rich history spanning nearly two centuries. In a recent breakthrough, the notorious Existence Conjecture for Combinatorial Designs dating back to the 1800s was proved in full by Keevash via the method of rando
Externí odkaz:
http://arxiv.org/abs/2402.17855
We study $k$-star decompositions, that is, partitions of the edge set into disjoint stars with $k$ edges, in the uniformly random $d$-regular graph model $\mathcal{G}_{n,d}$. We prove an existence result for such decompositions for all $d,k$ such tha
Externí odkaz:
http://arxiv.org/abs/2308.16037