P'eter Csikv'ari

activity

20182022

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

1 citations · 1 across the 2 of their papers we have counts for

collaborators

6 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.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.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.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…