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pro vyhledávání: '"Bohman, Tom"'
Autor:
Bohman, Tom, Hofstad, Jakob
We show that the independence number of $ G_{n,m}$ is concentrated on two values for $ n^{5/4+ \epsilon} < m \le \binom{n}{2}$. This result establishes a distinction between $G_{n,m}$ and $G_{n,p}$ with $p = m/ \binom{n}{2}$ in the regime $ n^{5/4 +
Externí odkaz:
http://arxiv.org/abs/2410.05420
We show that the domination number of the binomial random graph G_{n,p} with edge-probability p is concentrated on two values for p \ge n^{-2/3+\eps}, and not concentrated on two values for general p \le n^{-2/3}. This refutes a conjecture of Glebov,
Externí odkaz:
http://arxiv.org/abs/2401.10486
Autor:
Bohman, Tom, Hofstad, Jakob
We show that the independence number of $ G_{n,p}$ is concentrated on two values if $ n^{-2/3+ \epsilon} < p \le 1$. This result is roughly best possible as an argument of Sah and Sawhney shows that the independence number is not, in general, concent
Externí odkaz:
http://arxiv.org/abs/2208.00117
Autor:
Bohman, Tom, Hofstad, Jakob
The biclique partition number of a graph $G= (V,E)$, denoted $bp(G)$, is the minimum number of pairwise edge disjoint complete bipartite subgraphs of $G$ so that each edge of $G$ belongs to exactly one of them. It is easy to see that $ bp(G) \leq n -
Externí odkaz:
http://arxiv.org/abs/2206.13490
Autor:
Bohman, Tom, Newman, Andrew
The diameter of a strongly connected $d$-dimensional simplicial complex is the diameter of its dual graph. We provide a probabilistic proof of the existence of $d$-dimensional simplicial complexes with diameter $ (\frac{1}{d \cdot d!} - (\log n)^{-\e
Externí odkaz:
http://arxiv.org/abs/2204.11932
Autor:
Bohman, Tom, Peng, Fei
For $x$ real, let $ \{ x \}$ be the fractional part of $x$ (i.e. $\{x\} = x - \lfloor x \rfloor $). The lonely runner conjecture can be stated as follows: for any $n$ positive integers $ v_1 < v_2 < \dots < v_n $ there exists a real number $t$ such t
Externí odkaz:
http://arxiv.org/abs/2109.09860
Autor:
Bohman, Tom, Hofstad, Jakob
Publikováno v:
In Journal of Combinatorial Theory, Series B May 2024 166:50-79
Autor:
Bohman, Tom, Peng, Fei
Let $Q_n$ be the poset that consists of all subsets of a fixed $n$-element set, ordered by set inclusion. The poset cube Ramsey number $R(Q_n,Q_n)$ is defined as the least $m$ such that any 2-coloring of the elements of $Q_m$ admits a monochromatic c
Externí odkaz:
http://arxiv.org/abs/2102.00317
A $k$-uniform hypergraph with $n$ vertices is an $(n,k,\ell)$-omitting system if it does not contain two edges whose intersection has size exactly $\ell$. If in addition it does not contain two edges whose intersection has size greater than $\ell$, t
Externí odkaz:
http://arxiv.org/abs/2101.04258
Autor:
Bohman, Tom, Zhu, Emily
Let $\mathcal{H}$ be a 3-uniform hypergraph. The multicolor Ramsey number $ r_k(\mathcal{H})$ is the smallest integer $n$ such that every coloring of $ \binom{[n]}{3}$ with $k$ colors has a monochromatic copy of $\mathcal{H}$. Let $ \mathcal{L}$ be t
Externí odkaz:
http://arxiv.org/abs/1907.05236