Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Péter Csikvári"'
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:
Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) ISBN: 9781611977554
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::025c520fec7c70cff950b6a82a372643
https://doi.org/10.1137/1.9781611977554.ch29
https://doi.org/10.1137/1.9781611977554.ch29
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:
Péter Csikvári
Let $G$ be a triangle-free graph on $n$ vertices with adjacency matrix eigenvalues $\mu_1(G)\geq \mu_2(G)\geq \dots \geq \mu_n(G)$. In this paper we study the quantity $$\mu_1(G)+\mu_n(G).$$ We prove that for any triangle-free graph $G$ we have $$\mu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::674f38f2cb2148f1fa8a79c3c1470cb3
http://arxiv.org/abs/2205.08873
http://arxiv.org/abs/2205.08873
In this short note we show that a system $M=(E,r)$ with a ground set $E$ of size $m$ and (rank) function $r: 2^E\to \mathbb{Z}_{\geq 0}$ satisfying $r(S)\leq \min(r(E),|S|)$ for every set $S\subseteq E$, the Tutte polynomial $$T_M(x,y):=\sum_{S\subse
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f1c83c310789dd0f14945d9f32a330b9
http://arxiv.org/abs/2201.10404
http://arxiv.org/abs/2201.10404
Publikováno v:
The Electronic Journal of Combinatorics, 28(4):4-14. Electronic Journal of Combinatorics
We use Wagner's weighted subgraph counting polynomial to prove that the partition function of the anti-ferromagnetic Ising model on line graphs is real rooted and to prove that roots of the edge cover polynomial have absolute value at most 4. We more
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::25c677b2fa7dd6c9ae2223489af5d3a0
https://dare.uva.nl/personal/pure/en/publications/some-applications-of-wagners-weighted-subgraph-counting-polynomial(4d70fd4b-777a-4195-b65d-654d80dea62c).html
https://dare.uva.nl/personal/pure/en/publications/some-applications-of-wagners-weighted-subgraph-counting-polynomial(4d70fd4b-777a-4195-b65d-654d80dea62c).html
Publikováno v:
European Journal of Combinatorics. 62:70-76
Let H WR be the path on 3 vertices with a loop at each vertex. D. Galvin (Galvin, 2013, 2014) conjectured, and E. Cohen, W. Perkins and P. Tetali (Cohen et al., in press) proved that for any d -regular simple graph G on n vertices we have hom ( G , H
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fe5c099bd2453512ee4c47e580de7c45
https://doi.org/10.1016/j.ejc.2016.11.003
https://doi.org/10.1016/j.ejc.2016.11.003
Publikováno v:
ISIT
Graph covers and the Bethe free energy have been useful theoretical tools for producing lower bounds on a variety of counting problems in graphical models, including the permanent and the ferromagnetic Ising model. Here, we propose a new conjecture t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3bb7df125983cef55aff15ca6352dd30
https://doi.org/10.1109/isit.2019.8849389
https://doi.org/10.1109/isit.2019.8849389
Autor:
Péter Csikvári, András Imolay
Given a graph $G$ with only even degrees, let $\varepsilon(G)$ denote the number of Eulerian orientations, and let $h(G)$ denote the number of half graphs, that is, subgraphs $F$ such that $d_F(v)=d_G(v)/2$ for each vertex $v$. Recently, Borbényi an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fad6669c95ccaa6934866ba0f3ea561d
http://arxiv.org/abs/1905.06678
http://arxiv.org/abs/1905.06678