Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Borbényi, Márton"'
For a graph $G$ let $\varepsilon(G)$ denote the number of Eulerian orientations, and $v(G)$ denote the number of vertices of $G$. We show that if $(G_n)_n$ is a sequence of Eulerian graphs that are convergent in Benjamini--Schramm sense, then $\lim\l
Externí odkaz:
http://arxiv.org/abs/2409.18012
A recent line of research has concentrated on exploring the links between analytic and combinatorial theories of submodularity, uncovering several key connections between them. In this context, Lov\'asz initiated the study of matroids from an analyti
Externí odkaz:
http://arxiv.org/abs/2406.08945
We introduce the concept of quotient-convergence for sequences of submodular set functions, providing, among others, a new framework for the study of convergence of matroids through their rank functions. Extending the limit theory of bounded degree g
Externí odkaz:
http://arxiv.org/abs/2406.08942
Publikováno v:
Electron. J. Probab. 28: 1-45 (2023)
The random interlacement point process (introduced by Sznitman, generalized by Teixeira) is a Poisson point process on the space of labeled doubly infinite nearest neighbour trajectories modulo time-shift on a transient graph $G$. We show that the ra
Externí odkaz:
http://arxiv.org/abs/2208.14545
For a graph $G=(V,E)$ with $v(G)$ vertices the partition function of the random cluster model is defined by $$Z_G(q,w)=\sum_{A\subseteq E(G)}q^{k(A)}w^{|A|},$$ where $k(A)$ denotes the number of connected components of the graph $(V,A)$. Furthermore,
Externí odkaz:
http://arxiv.org/abs/2205.06565
Let $G$ be the Cartesian product of a regular tree $T$ and a finite connected transitive graph $H$. It is shown in arXiv:2006.06387 that the Free Uniform Spanning Forest ($\mathsf{FSF}$) of this graph may not be connected, but the dependence of this
Externí odkaz:
http://arxiv.org/abs/2011.12904
Autor:
Borbényi, Márton, Csikvári, Péter
For a graph $G$ on $v(G)$ vertices let $m_k(G)$ denote the number of matchings of size $k$, and consider the partition function $M_{G}(\lambda)=\sum_{k=0}^nm_k(G)\lambda^k$. In this paper we show that if $G$ is a $d$--regular graph and $0<\lambda<(4d
Externí odkaz:
http://arxiv.org/abs/2006.16815
Let $F(G)$ be the number of forests of a graph $G$. Similarly let $C(G)$ be the number of connected spanning subgraphs of a connected graph $G$. We bound $F(G)$ and $C(G)$ for regular graphs and for graphs with fixed average degree. Among many other
Externí odkaz:
http://arxiv.org/abs/2005.12752
Autor:
Borbényi, Márton, Csikvári, Péter
The goal of this short paper to advertise the method of gauge transformations (aka holographic reduction, reparametrization) that is well-known in statistical physics and computer science, but less known in combinatorics. As an application of it we g
Externí odkaz:
http://arxiv.org/abs/1905.06215
Autor:
Bencs, Ferenc1 (AUTHOR), Borbényi, Márton2,3 (AUTHOR), Csikvári, Péter2,3 (AUTHOR) peter.csikvari@gmail.com
Publikováno v:
Communications in Mathematical Physics. Apr2023, Vol. 399 Issue 1, p203-248. 46p.