Tibor Szab'o

activity

20232026

collaborators

11 papers

math.CO2026

Graph bootstrap percolation -- a discovery of slowness

David Fabian, Patrick Morris, Tibor Szabó

Graph bootstrap percolation is a discrete-time process capturing the spread of a virus on the edges of $K_{n}$ . Given an initial set $G \subseteq K_{n}$ of infected edges, the transmiss…

math.CO2026

The maximum diameter of $d$ -dimensional simplicial complexes

Stefan Glock, Olaf Parczyk, Silas Rathke +1

For every fixed dimension $d$ and sufficiently large $n$ , we determine the maximum possible diameter of a strongly connected $d$ -dimensional simplicial complex on $n$ vertices. Thi…

math.CO2025

The maximum diameter of 2-dimensional simplicial complexes

Olaf Parczyk, Silas Rathke, Tibor Szabó

We study a problem of Santos about the largest possible diameter of a $d$ -dimensional (abstract) simplicial complex on $n$ vertices. For dimension 2, we determine the exact value o…

math.CO2025

Improved bounds for the minimum degree of minimal multicolor Ramsey graphs

Yamaan Attwa, Sam Mattheus, Tibor Szabó +1

We provide two novel constructions of $r$ edge-disjoint $K_{k + 1}$ -free graphs on the same vertex set, each of which has the property that every small induced subgraph contains a co…

math.CO2025

Slow graph bootstrap percolation III: Chain constructions

David Fabian, Patrick Morris, Tibor Szabó

For graphs $H$ , we study the extremal function $M_{H} (n)$ which is the maximum running time (until stabilisation) of an $H$ -bootstrap percolation process on $n$ vertices. Building on…

math.CO2025

Almost-perfect colorful matchings in three-edge-colored bipartite graphs

Simona Boyadzhiyska, Micha Christoph, Tibor Szabó

We prove that, for positive integers $n, a_{1}, a_{2}, a_{3}$ satisfying $a_{1} + a_{2} + a_{3} = n - 1$ , it holds that any bipartite graph $G$ which is the union of three perfect matchings $M_{1}$ , $M…

math.CO2025

On almost Gallai colourings in complete graphs

Alexandr Grebennikov, Letícia Mattos, Tibor Szabó

For $t \in N$ , we say that a colouring of $E (K_{n})$ is $almost$ $t$ - $Gallai$ if no two rainbow $t$ -cliques share an edge. Motivated by a lemma of Berkowit…

math.CO2024

On the number of sets with small sumset

Dingyuan Liu, Letícia Mattos, Tibor Szabó

We investigate subsets with small sumset in arbitrary abelian groups. For an abelian group $G$ and an $n$ -element subset $Y \subseteq G$ we show that if $m ≪ s^{2} / (lo g n)^{2}$ , the…

math.CO2024

Global rigidity of random graphs in $R$

Richard Montgomery, Rajko Nenadov, Julien Portier +1

We investigate the problem of reconstructing a set $P \subseteq R$ of distinct points, where the only information available about $P$ consists of the distances between some…

math.CO2023

Slow graph bootstrap percolation II: Accelerating properties

David Fabian, Patrick Morris, Tibor Szabó

For a graph $H$ and an $n$ -vertex graph $G$ , the $H$ -bootstrap process on $G$ is the process which starts with $G$ and, at every time step, adds any missing edges on the vertices o…

math.CO2023

Slow graph bootstrap percolation I: Cycles

David Fabian, Patrick Morris, Tibor Szabó

Given a fixed graph $H$ and an $n$ -vertex graph $G$ , the $H$ \emph{-bootstrap percolation process} on $G$ is defined to be the sequence of graphs $G_{i}$ , $i \geq 0$ which starts with…

Graph bootstrap percolation -- a discovery of slowness

The maximum diameter of d-dimensional simplicial complexes

The maximum diameter of 2-dimensional simplicial complexes

Improved bounds for the minimum degree of minimal multicolor Ramsey graphs

Slow graph bootstrap percolation III: Chain constructions

Almost-perfect colorful matchings in three-edge-colored bipartite graphs

On almost Gallai colourings in complete graphs

On the number of sets with small sumset

Global rigidity of random graphs in R

Slow graph bootstrap percolation II: Accelerating properties

Slow graph bootstrap percolation I: Cycles

The maximum diameter of $d$ -dimensional simplicial complexes

Global rigidity of random graphs in $R$