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

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Showing 2022Show all

4 papers · 1 filter

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…