Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Versteegen, Leo"'
In 1995, Erd\H{o}s and Gy\'{a}rf\'{a}s proved that in every $2$-edge-coloured complete graph on $n$ vertices, there exists a collection of $2\sqrt{n}$ monochromatic paths, all of the same colour, which cover the entire vertex set. They conjectured th
Externí odkaz:
http://arxiv.org/abs/2409.03623
Let $G\sim G(n,p)$ be a (hidden) Erd\H{o}s-R\'enyi random graph with $p=(1+ \varepsilon)/n$ for some fixed constant $ \varepsilon >0$. Ferber, Krivelevich, Sudakov, and Vieira showed that to reveal a path of length $\ell=\Omega\left(\frac{\log(1/ \va
Externí odkaz:
http://arxiv.org/abs/2409.02812
The balance game is played on a graph $G$ by two players, Admirable (A) and Impish (I), who take turns selecting unlabeled vertices of $G$. Admirable labels the selected vertices by $0$ and Impish by $1$, and the resulting label on any edge is the su
Externí odkaz:
http://arxiv.org/abs/2409.01796
A graph $H$ is said to be positive if the homomorphism density $t_H(G)$ is non-negative for all weighted graphs $G$. The positive graph conjecture proposes a characterisation of such graphs, saying that a graph is positive if and only if it is symmet
Externí odkaz:
http://arxiv.org/abs/2404.17467
Autor:
Versteegen, Leo
A linear graph code is a family $\mathcal{C}$ of graphs on $n$ vertices with the property that the symmetric difference of the edge sets of any two graphs in $\mathcal{C}$ is also the edge set of a graph in $\mathcal{C}$. In this article, we investig
Externí odkaz:
http://arxiv.org/abs/2310.19891
Autor:
Versteegen, Leo
A graph $H$ is called strongly common if for every coloring $\phi$ of $K_n$ with two colors, the number of monochromatic copies of $H$ is at least the number of monochromatic copies of $H$ in a random coloring of $K_n$ with the same density of color
Externí odkaz:
http://arxiv.org/abs/2305.10903
An interval colouring of a graph $G=(V,E)$ is a proper colouring $c\colon E\to \mathbb{Z}$ such that the set of colours of edges incident to any given vertex forms an interval of $\mathbb{Z}$. The interval thickness $\theta(G)$ of a graph $G$ is the
Externí odkaz:
http://arxiv.org/abs/2303.05505
Autor:
Axenovich, Maria, Girão, António, Hollom, Lawrence, Portier, Julien, Powierski, Emil, Savery, Michael, Tamitegama, Youri, Versteegen, Leo
Publikováno v:
European Journal of Combinatorics, 120 (2024)
A graph is said to be interval colourable if it admits a proper edge-colouring using palette $\mathbb{N}$ in which the set of colours incident to each vertex is an interval. The interval colouring thickness of a graph $G$ is the minimum $k$ such that
Externí odkaz:
http://arxiv.org/abs/2303.04782
Autor:
Versteegen, Leo
A set $A\subset \mathbb{F}_p^n$ is sum-free if $A+A$ does not intersect $A$. If $p\equiv 2 \mod 3$, the maximal size of a sum-free in $\mathbb{F}_p^n$ is known to be $(p^n+p^{n-1})/3$. We show that if a sum-free set $A\subset \mathbb{F}_p^n$ has size
Externí odkaz:
http://arxiv.org/abs/2303.00828
Autor:
Portier, Julien, Versteegen, Leo
The domination game is played on a graph $G$ by two players, Dominator and Staller, who alternate in selecting vertices until each vertex in the graph $G$ is contained in the closed neighbourhood of the set of selected vertices. Dominator's aim is to
Externí odkaz:
http://arxiv.org/abs/2301.05202