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pro vyhledávání: '"Lefmann, Hanno"'
For positive integers $n$ and $r$, we consider $n$-vertex graphs with the maximum number of $r$-edge-colorings with no copy of a triangle where exactly two colors appear. We prove that, if $2 \leq r \leq 26$ and $n$ is sufficiently large, the maximum
Externí odkaz:
http://arxiv.org/abs/2209.06991
Hindman proved in 1979 that no matter how natural numbers are colored in r colors, for a fixed positive integer r, there is an infinite subset X of numbers and a color t such that for any finite non-empty subset X' of X, the color of the sum of eleme
Externí odkaz:
http://arxiv.org/abs/2109.10249
Publikováno v:
In Discrete Mathematics April 2024 347(4)
Given integers $r \geq 2$, $k \geq 3$ and $2 \leq s \leq \binom{k}{2}$, and a graph $G$, we consider $r$-edge-colorings of $G$ with no copy of a complete graph $K_k$ on $k$ vertices where $s$ or more colors appear, which are called $\mathcal{P}_{k,s}
Externí odkaz:
http://arxiv.org/abs/2103.11892
The Fano plane is the unique linear 3-uniform hypergraph on seven vertices and seven hyperedges. It was recently proved that, for all $n \geq 8$, the balanced complete bipartite 3-uniform hypergraph on $n$ vertices, denoted by $B_n$, is the 3-uniform
Externí odkaz:
http://arxiv.org/abs/2006.00292
In this note, we adapt the Keevash-Sudakov proof of the (Tur\'{a}n) Stability Theorem for the Fano plane to find an explicit dependency between the parameters $\varepsilon$ and $\delta$. This is useful in the solution of a multicolored version for hy
Externí odkaz:
http://arxiv.org/abs/2004.11828
Given a family of graphs $\mathcal{F}$, we prove that the normalized edit distance of any given graph $\Gamma$ to being induced $\mathcal{F}$-free is estimable with a query complexity that depends only on the bounds of the Frieze--Kannan Regularity L
Externí odkaz:
http://arxiv.org/abs/1912.01081
Publikováno v:
In Discrete Applied Mathematics 15 July 2023 333:151-164
Publikováno v:
Combinator. Probab. Comp. 29 (2020) 616-632
There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the input. Gra
Externí odkaz:
http://arxiv.org/abs/1707.08225
Autor:
Lee, Sang June, Lefmann, Hanno
We prove the following: Fix an integer $k\geq 2$, and let $T$ be a real number with $T\geq 1.5$. Let $\cH=(V,\cE_2\cup \cE_3\cup\dots\cup\cE_k)$ be a non-uniform hypergraph with the vertex set $V$ and the set $\cE_i$ of edges of size $i=2,\ldots , k$
Externí odkaz:
http://arxiv.org/abs/1602.03569