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pro vyhledávání: '"Katona, Gyula O. H."'
For a family of sets $\mathcal{F}$, let $\omega(\mathcal{F}):=\sum_{\{A,B\}\subset \mathcal{F}}|A\cap B|$. In this paper, we prove that provided $n$ is sufficiently large, for any $\mathcal{F}\subset \binom{[n]}{k}$ with $|\mathcal{F}|=m$, $\omega(\m
Externí odkaz:
http://arxiv.org/abs/2407.12171
Autor:
Katona, Gyula O. H., Katona, Gyula Y.
A $(k,\ell )$ partial partition of an $n$-element set is a collection of $\ell $ pairwise disjoint $k$-element subsets. It is proved that, if $n$ is large enough, one can find $\left\lfloor {n\choose k}/{\ell}\right\rfloor$ such partial partitions in
Externí odkaz:
http://arxiv.org/abs/2312.09134
Autor:
Katona, Gyula O. H., Xiao, Jimeng
Suppose $k \ge 2$ is an integer. Let $Y_k$ be the poset with elements $x_1, x_2, y_1, y_2, \ldots, y_{k-1}$ such that $y_1 < y_2 < \cdots < y_{k-1} < x_1, x_2$ and let $Y_k'$ be the same poset but all relations reversed. We say that a family of subse
Externí odkaz:
http://arxiv.org/abs/2003.08238
Autor:
Xiao, Chuanqi, Katona, Gyula O. H.
By the theorem of Mantel $[5]$ it is known that a graph with $n$ vertices and $\lfloor \frac{n^{2}}{4} \rfloor+1$ edges must contain a triangle. A theorem of Erd\H{o}s gives a strengthening: there are not only one, but at least $\lfloor\frac{n}{2}\rf
Externí odkaz:
http://arxiv.org/abs/2003.04450
Given a graph $G$ and a positive integer $k$, the \emph{Gallai-Ramsey number} is defined to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) copy of $G$ or a monochromati
Externí odkaz:
http://arxiv.org/abs/2001.02789
The Tur\'an number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. Let P_k be the path with k vertices, the square P^2_k of P_k is obtained by joining the pairs of vertices with dist
Externí odkaz:
http://arxiv.org/abs/1912.02726
Consider all $k$-element subsets and $\ell$-element subsets $(k>\ell )$ of an $n$-element set as vertices of a bipartite graph. Two vertices are adjacent if the corresponding $\ell$-element set is a subset of the corresponding $k$-element set. Let $G
Externí odkaz:
http://arxiv.org/abs/1910.10876
Autor:
Damásdi, Gábor, Gerbner, Dániel, Katona, Gyula O. H., Keszegh, Balázs, Lenger, Dániel, Methuku, Abhishek, Nagy, Dániel T., Pálvölgyi, Dömötör, Patkós, Balázs, Vizer, Máté, Wiener, Gábor
Suppose that the vertices of a graph $G$ are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We
Externí odkaz:
http://arxiv.org/abs/1903.08383
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