Zobrazeno 1 - 4
of 4
pro vyhledávání: '"Márton Borbényi"'
Autor:
Márton Borbényi, Peter Csikvari
Publikováno v:
Transactions on Combinatorics, Vol 10, Iss 2, Pp 73-95 (2021)
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
Externí odkaz:
https://doaj.org/article/f653ed4bd22e41d79b4391c0ef112ea8
Publikováno v:
Communications in Mathematical Physics. 399:203-248
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::87df769e8aa30a2f6a8de06d71b3a649
https://doi.org/10.1007/s00220-022-04552-1
https://doi.org/10.1007/s00220-022-04552-1
Publikováno v:
Graphs and Combinatorics. 37:2655-2678
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 a fixed average degree. Among many other things we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cb47117a8442422e7067e3ab20040c1b
https://doi.org/10.1007/s00373-021-02382-x
https://doi.org/10.1007/s00373-021-02382-x
Autor:
Márton Borbényi, Péter Csikvári
Publikováno v:
Discrete Mathematics
The goal of this paper is 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 give
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::775a52bdac02ea295619b1f059af747c
http://arxiv.org/abs/1905.06215
http://arxiv.org/abs/1905.06215
