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of 475
pro vyhledávání: '"Kühn, Daniela"'
For all integers $n \geq k > d \geq 1$, let $m_{d}(k,n)$ be the minimum integer $D \geq 0$ such that every $k$-uniform $n$-vertex hypergraph $\mathcal H$ with minimum $d$-degree $\delta_{d}(\mathcal H)$ at least $D$ has an optimal matching. For every
Externí odkaz:
http://arxiv.org/abs/2211.01325
We prove that for $n \in \mathbb N$ and an absolute constant $C$, if $p \geq C\log^2 n / n$ and $L_{i,j} \subseteq [n]$ is a random subset of $[n]$ where each $k\in [n]$ is included in $L_{i,j}$ independently with probability $p$ for each $i, j\in [n
Externí odkaz:
http://arxiv.org/abs/2206.14472
In 1977, Erd\H{o}s asked the following question: for any integers $t,n \in \mathbb{N}$, if $G_1 , \dots , G_n$ are complete graphs such that each $G_i$ has at most $n$ vertices and every pair of them shares at most $t$ vertices, what is the largest p
Externí odkaz:
http://arxiv.org/abs/2110.06181
Suppose a $k$-uniform hypergraph $H$ that satisfies a certain regularity instance (that is, there is a partition of $H$ given by the hypergraph regularity lemma into a bounded number of quasirandom subhypergraphs of prescribed densities). We prove th
Externí odkaz:
http://arxiv.org/abs/2110.01570
A collection of graphs is \textit{nearly disjoint} if every pair of them intersects in at most one vertex. We prove that if $G_1, \dots, G_m$ are nearly disjoint graphs of maximum degree at most $D$, then the following holds. For every fixed $C$, if
Externí odkaz:
http://arxiv.org/abs/2109.11438
This paper provides a survey of methods, results, and open problems on graph and hypergraph colourings, with a particular emphasis on semi-random `nibble' methods. We also give a detailed sketch of some aspects of the recent proof of the Erd\H{o}s-Fa
Externí odkaz:
http://arxiv.org/abs/2106.13733
The Erd\H{o}s-Faber-Lov\'{a}sz conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In this paper, we prove this conjecture for every large $n$. We also provide stability versions of this
Externí odkaz:
http://arxiv.org/abs/2101.04698
Autor:
Goertz-Allmann, Bettina P., Langet, Nadège, Iranpour, Kamran, Kühn, Daniela, Baird, Alan, Oates, Steve, Rowe, Carrie, Harvey, Stephen, Oye, Volker, Nakstad, Hilde
Publikováno v:
In International Journal of Greenhouse Gas Control March 2024 133
Publikováno v:
Proc. London Math. Soc., 126 (2023): 429-517
In 1976, Alspach, Mason, and Pullman conjectured that any tournament $T$ of even order can be decomposed into exactly ${\rm ex}(T)$ paths, where ${\rm ex}(T):= \frac{1}{2}\sum_{v\in V(T)}|d_T^+(v)-d_T^-(v)|$. We prove this conjecture for all sufficie
Externí odkaz:
http://arxiv.org/abs/2010.14158
Publikováno v:
J. Lond. Math. Soc. (2), 108(5):1701-1746, 2023
Let $H$ be a $k$-uniform $D$-regular simple hypergraph on $N$ vertices. Based on an analysis of the R\"odl nibble, Alon, Kim and Spencer (1997) proved that if $k \ge 3$, then $H$ contains a matching covering all but at most $ND^{-1/(k-1)+o(1)}$ verti
Externí odkaz:
http://arxiv.org/abs/2010.04183