6 papers
The least balanced graphs and trees
Péter Csikvári, Viktor Harangi
Given a connected graph, the principal eigenvector of the adjacency matrix (often called the Perron vector) can be used to assign positive weights to the vertices. A natural way to…
Some bounds on the spectral radius of connected threshold graphs
Péter Csikvári, Ivan Damnjanović, Dragan Stevanović +1
The spectral radius of a graph is the spectral radius of its adjacency matrix. A threshold graph is a simple graph whose vertices can be ordered as , so that…
Number of Eulerian orientations for Benjamini--Schramm convergent graph sequences
Ferenc Bencs, Márton Borbényi, Péter Csikvári
For a graph let denote the number of Eulerian orientations, and denote the number of vertices of . We show that if is a sequence of Euleria…
Extremal number of arborescences
Aditya Bandekar, Péter Csikvári, Benjamin Mascuch +3
In this paper we study the following extremal graph theoretic problem: Given an undirected Eulerian graph , which Eulerian orientation minimizes or maximizes the number of arbor…
Short survey on stable polynomials, orientations and matchings
Péter Csikvári, Ádám Schweitzer
This is a short survey about the theory of stable polynomials and its applications. It gives self-contained proofs of two theorems of Schrijver. One of them asserts that for a -…
On Sidorenko's conjecture for determinants and Gaussian Markov random fields
Péter Csikvári, Balázs Szegedy
We study a class of determinant inequalities that are closely related to Sidorenko's famous conjecture (Also conjectured by Erd\H os and Simonovits in a different form). Our main r…