Zobrazeno 1 - 10
of 199
pro vyhledávání: '"Gyori, Ervin"'
Let $\mathcal{F}$ be a family of $r$-uniform hypergraphs. Denote by $\ex^{\mathrm{conn}}_r(n,\mathcal{F})$ the maximum number of hyperedges in an $n$-vertex connected $r$-uniform hypergraph which contains no member of $\mathcal{F}$ as a subhypergraph
Externí odkaz:
http://arxiv.org/abs/2409.03323
There are two particular $\Theta_6$-graphs - the 6-cycle graphs with a diagonal. We find the planar Tur\'an number of each of them, i.e. the maximum number of edges in a planar graph $G$ of $n$ vertices not containing the given $\Theta_6$ as a subgra
Externí odkaz:
http://arxiv.org/abs/2406.19584
Autor:
Győri, Ervin, Karim, Hilal Hama
Given two graphs $H$ and $F$, the generalized planar Tur\'an number $\mathrm{ex}_\mathcal{P}(n,H,F)$ is the maximum number of copies of $H$ that an $n$-vertex $F$-free planar graph can have. We investigate this function when $H$ and $F$ are short cyc
Externí odkaz:
http://arxiv.org/abs/2405.08162
A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. Let $G$ and $H$ be two graphs. The anti-Ramsey number $\ar(G, H)$ is the maximum number of colors of an edge-coloring of $G$ that does not contain a rainbow cop
Externí odkaz:
http://arxiv.org/abs/2401.01766
Bollob\'as proved that for every $k$ and $\ell$ such that $k\mathbb{Z}+\ell$ contains an even number, an $n$-vertex graph containing no cycle of length $\ell \bmod k$ can contain at most a linear number of edges. The precise (or asymptotic) value of
Externí odkaz:
http://arxiv.org/abs/2312.09999
Chung and Graham considered the problem of minimizing the number of edges in an $n$-vertex graph containing all $n$-vertex trees as a subgraph. They showed that such a graph has at least $\frac{1}{2}n \log{n}$ edges. In this note, we improve this low
Externí odkaz:
http://arxiv.org/abs/2311.01488
Autor:
Bärnkopf, Pál, Győri, Ervin
We consider the problem of extending partial edge colorings of (iterated) cartesian products of even cycles and paths, focusing on the case when the precolored edges constitute a matching. We prove the conjecture of Casselgren, Granholm and Petros th
Externí odkaz:
http://arxiv.org/abs/2310.09973
A graph is outerplanar if it has a planar drawing for which all vertices belong to the outer face of the drawing. Let $H$ be a graph. The outerplanar Tur\'an number of $H$, denoted by $ex_\mathcal{OP}(n,H)$, is the maximum number of edges in an $n$-v
Externí odkaz:
http://arxiv.org/abs/2310.00557
The generalized Tur\'an number $\ex(n,K_s,F)$ denotes the maximum number of copies of $K_s$ in an $n$-vertex $F$-free graph. Let $kF$ denote $k$ disjoint copies of $F$. Gerbner, Methuku and Vizer [DM, 2019, 3130-3141] gave a lower bound for $\ex(n,K_
Externí odkaz:
http://arxiv.org/abs/2309.09603
Let $\mathcal{H}$ be a set of graphs. The planar Tur\'an number, $ex_\mathcal{P}(n,\mathcal{H})$, is the maximum number of edges in an $n$-vertex planar graph which does not contain any member of $\mathcal{H}$ as a subgraph. When $\mathcal{H}=\{H\}$
Externí odkaz:
http://arxiv.org/abs/2308.09185