Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Araújo, Igor P."'
Autor:
Araujo, Igor, Peng, Dadong
Erd\H{o}s and Rado [P. Erd\H{o}s, R. Rado, A combinatorial theorem, Journal of the London Mathematical Society 25 (4) (1950) 249-255] introduced the Canonical Ramsey numbers $\text{er}(t)$ as the minimum number $n$ such that every edge-coloring of th
Externí odkaz:
http://arxiv.org/abs/2409.11574
Given graphs $F$ and $G$, a perfect $F$-tiling in $G$ is a collection of vertex-disjoint copies of $F$ in $G$ that together cover all the vertices in $G$. The study of the minimum degree threshold forcing a perfect $F$-tiling in a graph $G$ has a lon
Externí odkaz:
http://arxiv.org/abs/2305.07294
Autor:
Araujo, Igor, Frederickson, Bryce, Krueger, Robert A., Lidický, Bernard, McAllister, Tyrrell B., Pfender, Florian, Spiro, Sam, Stucky, Eric Nathan
We consider a geometric percolation process partially motivated by recent work of Hejda and Kala. Specifically, we start with an initial set $X \subseteq \mathbb{Z}^2$, and then iteratively check whether there exists a triangle $T \subseteq \mathbb{R
Externí odkaz:
http://arxiv.org/abs/2303.15402
Autor:
Araujo, Igor, Black, Alexander E., Burcroff, Amanda, Gao, Yibo, Krueger, Robert A., McDonough, Alex
Given two vectors $u$ and $v$, their outer sum is given by the matrix $A$ with entries $A_{ij} = u_{i} + v_{j}$. If the entries of $u$ and $v$ are increasing and sufficiently generic, the total ordering of the entries of the matrix is a standard Youn
Externí odkaz:
http://arxiv.org/abs/2302.09194
In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every $\alpha>0$, there exists a constant $C$ such that for every $n$-vertex digraph of minimum semi-degree at least
Externí odkaz:
http://arxiv.org/abs/2212.10112
A path in an edge-colored graph is said to be rainbow if no color repeats on it. An edge-colored graph is said to be rainbow $k$-connected if every pair of vertices is connected by $k$ internally disjoint rainbow paths. The rainbow $k$-connection num
Externí odkaz:
http://arxiv.org/abs/2210.12291
An essential cover of the vertices of the $n$-cube $\{0,1\}^n$ by hyperplanes is a minimal covering where no hyperplane is redundant and every variable appears in the equation of at least one hyperplane. Linial and Radhakrishnan gave a construction o
Externí odkaz:
http://arxiv.org/abs/2209.00140
Denote by $F_5$ the $3$-uniform hypergraph on vertex set $\{1,2,3,4,5\}$ with hyperedges $\{123,124,345\}$. Balogh, Butterfield, Hu, and Lenz proved that if $p > K \log n / n$ for some large constant $K$, then every maximum $F_5$-free subhypergraph o
Externí odkaz:
http://arxiv.org/abs/2203.02826
We count the ordered sum-free triplets of subsets in the group $\mathbb{Z}/p\mathbb{Z}$, i.e., the triplets $(A,B,C)$ of sets $A,B,C \subset \mathbb{Z}/p\mathbb{Z}$ for which the equation $a+b=c$ has no solution with $a\in A$, $b \in B$ and $c \in C$
Externí odkaz:
http://arxiv.org/abs/2101.05914
We prove that the maximum determinant of an $n \times n $ matrix, with entries in $\{0,1\}$ and at most $n+k$ non-zero entries, is at most $2^{k/3}$, which is best possible when $k$ is a multiple of 3. This result solves a conjecture of Bruhn and Rau
Externí odkaz:
http://arxiv.org/abs/2011.01892