Balázs Patkós

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4 papers · 1 filter

math.CO2026

On the damage number of graphs

Valentin Gledel, William B. Kinnersley, Balázs Patkós +1

We study a variant of Cops and Robbers in which the robber attempts to visit as many vertices of the graph as possible without being captured, while the cop aims to keep the robber…

math.CO2022

On graphs that contain exactly k copies of a subgraph, and a related problem in search theory

Dániel Gerbner, Balázs Keszegh, Dániel Lenger +5

We study $exa_{k} (n, F)$ , the largest number of edges in an $n$ -vertex graph $G$ that contains exactly $k$ copies of a given subgraph $F$ . The case $k = 0$ is the Turán number…

math.CO2022

On the number of maximal independent sets: From Moon-Moser to Hujter-Tuza

Cory Palmer, Balázs Patkós

We connect two classical results in extremal graph theory concerning the number of maximal independent sets. The maximum number mis $(n)$ of maximal independent sets in an $n$ -verte…

math.CO2022

Triangles in intersecting families

Dániel T. Nagy, Balázs Patkós

We prove the following the generalized Turán type result. A collection $T$ of $r$ sets is an $r$ -triangle if for every $T_{1}, T_{2}, \dots, T_{r - 1} \in T$ we have $\ca…