P'eter Csikv'ari

activity

20142022

most citedExtremal regular graphs: the case of the infinite regular tree

10 citations · 16 across the 10 of their papers we have counts for

collaborators

13 papers

math.CO2022★ 1 cited

Note on the sum of the smallest and largest eigenvalues of a triangle-free graph

Péter Csikvári

Let $G$ be a triangle-free graph on $n$ vertices with adjacency matrix eigenvalues $μ_{1} (G) \geq μ_{2} (G) \geq \dots \geq μ_{n} (G)$ . In this paper we study the quantity $μ_{1} (G) + μ_{n} (G) .$ …

math.CO2022★ 3 cited

Random cluster model on regular graphs

Ferenc Bencs, Márton Borbényi, Péter Csikvári

For a graph $G = (V, E)$ with $v (G)$ vertices the partition function of the random cluster model is defined by $Z_{G} (q, w) = A \subseteq E (G) \sum q^{k (A)} w^{∣ A ∣},$ where $k (A)$ denotes…

cs.DM2022

On complex roots of the independence polynomial

Ferenc Bencs, Péter Csikvári, Piyush Srivastava +1

It is known from the work of Shearer (1985) (and also Scott and Sokal (2005)) that the independence polynomial $Z_{G} (λ)$ of a graph $G$ of maximum degree at most $d + 1$ does not vani…

math.CO2022

Short proof of a theorem of Brylawski on the coefficients of the Tutte polynomial

Csongor Beke, Gergely Kál Csáji, Péter Csikvári +1

In this short note we show that a system $M = (E, r)$ with a ground set $E$ of size $m$ and (rank) function $r : 2^{E} \to Z_{\geq 0}$ satisfying $r (S) \leq min (r (E), ∣ S ∣)$ for ev…

math.CO2021

Evaluations of Tutte polynomials of regular graphs

Ferenc Bencs, Péter Csikvári

Let $T_{G} (x, y)$ be the Tutte polynomial of a graph $G$ . In this paper we show that if $(G_{n})_{n}$ is a sequence of $d$ -regular graphs with girth $g (G_{n}) \to \infty$ , then for $x \geq 1$ …

math.CO2021

Upper bound for the number of spanning forests of regular graphs

Ferenc Bencs, Péter Csikvári

We show that if $G$ is a $d$ --regular graph on $n$ vertices, then the number of spanning forests $F (G)$ satisfies $F (G) \leq d^{n}$ . The previous best bound due to Kahale and Schulman…

math.CO2020

Matchings in regular graphs: minimizing the partition function

Márton Borbényi, Péter Csikvári

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 $M_{G} (λ) = \sum_{k = 0}^{n} m_{k} (G) λ^{k}$ . In this paper we s…

math.CO2020★ 2 cited

On the number of forests and connected spanning subgraphs

Márton Borbényi, Péter Csikvári, Haoran Luo

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 regu…

math.CO2019

Covers, orientations and factors

Péter Csikvári, András Imolay

Given a graph $G$ with only even degrees let $ε (G)$ denote the number of Eulerian orientations, and let $h (G)$ denote the number of half graphs, that is, subgraphs $F$ su…

math.CO2019

Counting degree-constrained subgraphs and orientations

Márton Borbényi, Péter Csikvári

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…

math.CO2018

Note on the zero-free region of the hard-core model

Ferenc Bencs, Péter Csikvári

In this paper we prove a new zero-free region for the partition function of the hard-core model, that is, the independence polynomials of graphs with largest degree $Δ$ . This new d…

math.CO2016★ 10 cited

Extremal regular graphs: the case of the infinite regular tree

Péter Csikvári

In this paper we study the following problem. Let $A$ be a fixed graph, and let $hom (G, A)$ denote the number of homomorphisms from a graph $G$ to $A$ . Furthermore, let $v (G)$ deno…

math.CO2014

Matchings in Benjamini-Schramm convergent graph sequences

Miklos Abért, Péter Csikvári, Péter Frenkel +1

We introduce the matching measure of a finite graph as the uniform distribution on the roots of the matching polynomial of the graph. We analyze the asymptotic behavior of the matc…