Tamás Csernák

activity

20212026

collaborators

9 papers

math.CO2026

An asymptotically tight bound on oriented diameter

Jiangdong Ai, Yaojun Chen, Yaokun Feng +5

Let $f (d)$ be the smallest integer such that every finite connected bridgeless simple graph of diameter $d$ admits a strong orientation of diameter at most $f (d)$ . Chvátal and Thom…

math.CO2026

Stacking and Clearing in Directed Graph Pebbling

Tamás Csernák, Lajos Soukup

Suppose that pebbles are distributed on the vertices of a directed graph D. A directed pebbling step u -> v along an arc u -> v removes two pebbles from u and places one pebble on…

math.CO2026

Stacking and clearing in graph pebbling

Tamás Csernák, Lajos Soukup

Suppose that pebbles are distributed on the vertices of a graph G. A pebbling step along an edge uv removes two pebbles from u and places one pebble on v. We introduce two new grap…

math.GN2025

Cut-and-choose games in topological spaces

Lucas Chiozini, Tamás Csernák, Lajos Soukup

We study transfinite cut-and-choose games on $T_{0}$ spaces, introducing the {\em point-separating number} $p s (X)$ and the {\em set membership number} $s m (X)$ as the ordinal-valued…

math.CO2023

Trivial coloring of Cartesian product of graphs

Tamás Csernák

A coloring of a direct product of graphs is said to be {\em trivial} iff it is induced by some coloring of a factor of the product. A graph $G$ is trivially power colorable iff eve…

math.CO2022

On Proper Colorings of Functions

Tamás Csernák

We investigate the infinite version of the $k$ -switch problem of Greenwell and Lovász. Given infinite cardinals $κ$ and $λ$ , for functions $x, y \in^{λ} κ$ we say that they are total…

math.CO2022

List Chromatic Number of Finitary Matroids: A Generalization of Seymour's Result

Tamás Csernák

Seymour proved that the chromatic numbers and the list chromatic numbers of loop-free finite matroids are the same. In this paper we prove the same statement for infinite, loop-fre…

math.LO2022

Infinite Combinatorics revisited in the absence of Axiom of Choice

Tamás Csernák, Lajos Soukup

We investigate the provability of classical combinatorial theorems in ZF. Using combinatorial arguments, we establish the following results for each infinite cardinal $κ \in O n$ , (1…

math.LO2021

Minimal vertex covers in infinite hypergraphs

Tamás Csernák, Lajos Soukup

In this paper a hypergraph will be identified with the family of its edges. A hypergraph $E$ possesses property $C (k, ρ)$ iff $∣ ⋂ E^{'} ∣ < ρ$ for each $\mathcal E…