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pro vyhledávání: '"Tomon, Istv��n"'
For a positive integer $t$, let $F_t$ denote the graph of the $t\times t$ grid. Motivated by a 50-year-old conjecture of Erd��s about Tur��n numbers of $r$-degenerate graphs, we prove that there exists a constant $C=C(t)$ such that $\mathrm{e
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https://explore.openaire.eu/search/publication?articleId=doi_________::2384e896966f2b730557ab9e3c30efd8
Recently, the first two authors proved the Alon-Jaeger-Tarsi conjecture on non-vanishing linear maps, for large primes. We extend their ideas to address several other related conjectures. We prove the weak Additive Basis conjecture proposed by Szeged
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::21fcf5d63dd796da3704d5d00533c4b8
Autor:
Tomon, Istv��n, Zakharov, Dmitriy
In this short note, we prove the following analog of the K��v��ri-S��s-Tur��n theorem for intersection graphs of boxes. If $G$ is the intersection graph of $n$ axis-parallel boxes in $\mathbb{R}^{d}$ such that $G$ contains no copy of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3bfc6c97d0bc76a91abd6bed9ff5c388
Autor:
Pach, J��nos, Tomon, Istv��n
An ordered graph is a graph with a linear ordering on its vertex set. We prove that for every positive integer $k$, there exists a constant $c_k>0$ such that any ordered graph $G$ on $n$ vertices with the property that neither $G$ nor its complement
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https://explore.openaire.eu/search/publication?articleId=doi_________::a87eb3e3338a51cdaaef360a0540c6a0
Autor:
Tomon, Istv��n
A string graph is the intersection graph of curves in the plane. We prove that there exists an absolute constant $c>0$ such that if $G$ is a string graph on $n$ vertices, then $G$ contains either a clique or an independent set of size at least $n^{c}
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https://explore.openaire.eu/search/publication?articleId=doi_________::98942150cc2a9d7b02be62eeed7d5e7f
Autor:
Sudakov, Benny, Tomon, Istv��n
The extremal number of a graph $H$, denoted by $\mbox{ex}(n,H)$, is the maximum number of edges in a graph on $n$ vertices that does not contain $H$. The celebrated K��v��ri-S��s-Tur��n theorem says that for a complete bipartite graph
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bc9a17477798059636a7c92ed4d1a9d9
Autor:
Pach, J��nos, Tomon, Istv��n
If we want to color $1,2,\ldots,n$ with the property that all 3-term arithmetic progressions are rainbow (that is, their elements receive 3 distinct colors), then, obviously, we need to use at least $n/2$ colors. Surprisingly, much fewer colors suffi
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Two subsets $A,B$ of an $n$-element ground set $X$ are said to be \emph{crossing}, if none of the four sets $A\cap B$, $A\setminus B$, $B\setminus A$ and $X\setminus(A\cup B)$ are empty. It was conjectured by Karzanov and Lomonosov forty years ago th
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e76ada332c7904336eef890a7a86d1b
http://arxiv.org/abs/1704.02175
http://arxiv.org/abs/1704.02175
Autor:
Gy��ri, Ervin, Kor��ndi, D��niel, Methuku, Abhishek, Tomon, Istv��n, Tompkins, Casey, Vizer, M��t��
A classical result of Bondy and Simonovits in extremal graph theory states that if a graph on $n$ vertices contains no cycle of length $2k$ then it has at most $O(n^{1+1/k})$ edges. However, matching lower bounds are only known for $k=2,3,5$. In this
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e5256a99b72b018240a53871905d8094
An ordered graph $H$ is a simple graph with a linear order on its vertex set. The corresponding Tur��n problem, first studied by Pach and Tardos, asks for the maximum number $\text{ex}_ n^{1+\varepsilon}$ for some positive $\varepsilon=\varepsilo
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https://explore.openaire.eu/search/publication?articleId=doi_________::1c66d49e1a6863d4fec5fb98fa4c3b06