Zobrazeno 1 - 10
of 206
pro vyhledávání: '"Hladky, Jan"'
Autor:
Garbe, Frederik, Hladký, Jan
It is well-known that if $(A,B)$ is an $\tfrac{\varepsilon}{2}$-regular pair (in the sense of Szemer\'edi) then there exist sets $A'\subset A$ and $B'\subset B'$ with $|A'|\leq \varepsilon|A|$ and $|B'|\leq \varepsilon|B|$ so that the degrees of all
Externí odkaz:
http://arxiv.org/abs/2410.05023
In their study of the giant component in inhomogeneous random graphs, Bollob\'as, Janson, and Riordan introduced a class of branching processes parametrized by a possibly unbounded graphon. We prove that two such branching processes have the same dis
Externí odkaz:
http://arxiv.org/abs/2408.02528
Autor:
Hladký, Jan, Viswanathan, Gopal
A theorem of Frieze from 1985 asserts that the total weight of the minimum spanning tree of the complete graph $K_n$ whose edges get independent weights from the distribution $UNIFORM[0,1]$ converges to Ap\'ery's constant in probability, as $n\to\inf
Externí odkaz:
http://arxiv.org/abs/2310.11705
Autor:
Hladký, Jan, Viswanathan, Gopal
Each graphon $W:\Omega^2\rightarrow[0,1]$ yields an inhomogeneous random graph model $G(n,W)$. We show that $G(n,W)$ is asymptotically almost surely connected if and only if (i) $W$ is a connected graphon and (ii) the measure of elements of $\Omega$
Externí odkaz:
http://arxiv.org/abs/2305.03607
Autor:
Hladký, Jan, Hng, Eng Keat
Greb\'ik and Rocha [Fractional Isomorphism of Graphons, Combinatorica 42, pp 365-404 (2022)] extended the well studied notion of fractional isomorphism of graphs to graphons. We prove that fractionally isomorphic graphons can be approximated in the c
Externí odkaz:
http://arxiv.org/abs/2210.14097
Publikováno v:
Random Structures & Algorithms, volume 65 (2024), issue 1, pages 46-60
The theory of limits of permutations leads to limit objects called permutons, which are certain Borel measures on the unit square. We prove that permutons avoiding a given permutation of order $k$ have a particularly simple structure. Namely, almost
Externí odkaz:
http://arxiv.org/abs/2208.12712
Publikováno v:
Random Structures & Algorithms, volume 64 (2024), issue 3, pages 692-740
Flip processes, introduced in [Garbe, Hladk\'y, \v{S}ileikis, Skerman: From flip processes to dynamical systems on graphons], are a class of random graph processes defined using a rule which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \m
Externí odkaz:
http://arxiv.org/abs/2206.03884
We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself
Externí odkaz:
http://arxiv.org/abs/2201.12272
We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any trees such that $T_i$ has $i$ vertices and maximum degree at most $cn/\log n$, then $\{T_1,\dots,T_n\}$ packs into $K_n$. Our main result actually allow
Externí odkaz:
http://arxiv.org/abs/2106.11720
Publikováno v:
Discrete Analysis 2023:8
We develop a limit theory of Latin squares, paralleling the recent limit theories of dense graphs and permutations. We introduce a notion of density, an appropriate version of the cut distance, and a space of limit objects - so-called Latinons. Key r
Externí odkaz:
http://arxiv.org/abs/2010.07854