Levente Bodnár

activity

20242026

collaborators

13 papers

math.CO2026

The quadratic Brown--Erdős--Sós problem for 3-uniform hypergraphs with 8 and 9 edges

Levente Bodnár, Oleg Pikhurko, Shumin Sun +2

The famous and actively studied problem of Brown--Erdős--Sós from 1973 asks for $f^{(r)} (n; s, k)$ , the maximum number of edges in an $r$ -graph with $n$ vertices in which no $s$ vert…

math.CO2026

The inducibility of 6-vertex graphs

Levente Bodnár, Jun Gao, Jared León +3

The inducibility constant $λ_{F}$ of a graph $F$ is the asymptotically maximum induced density of $F$ in a growing sequence of graphs. This paper systematically investigates the ca…

math.CO2026

Strong non-principality of positive codegree Turán density

Levente Bodnár, Jun Gao, Oleg Pikhurko +2

The \emph{minimum positive codegree} $δ_{k - 1}^{+} (G)$ of a $k$ -graph $G$ is the minimum, over all $(k - 1)$ -sets that lie in at least one edge, of the number of edges containing that s…

math.CO2026

On problems of Erdős and Baumann-Briggs on minimising the density of $s$ -cliques in graphs with forbidden subgraphs

Levente Bodnár, Oleg Pikhurko

Using flag algebras, we prove that the minimum density of $8$ -cliques in a large graph without an independent set of size $3$ is $491411/268435456 + o (1)$ , thus resolving a new case…

math.CO2026

FlagAlgebraToolbox: Flag Algebra Computations in SageMath

Levente Bodnár

We introduce FlagAlgebraToolbox, an extension of SageMath capable of automating flag algebra calculations and optimizations. FlagAlgebraToolbox has a simple interface, can handle a…

math.CO2025

Tetrahedron Conjecture in the $ℓ_{2}$ -norm

Levente Bodnár, Wanfang Chen, Jinghua Deng +5

The famous Tetrahedron Conjecture of Turán from the 1940s asserts that the number of edges in an $n$ -vertex $3$ -graph without the tetrahedron, the complete $3$ -graph on four vertic…

math.CO2025

Semi-inducibility of 4-vertex graphs

Levente Bodnár, Oleg Pikhurko

For a graph $H$ whose edges are coloured blue or red, the $H$ -semi-inducibility problem asks for the maximum, over all graphs $G$ of given order $n$ , of the number of injections fr…

math.CO2025

Some exact inducibility-type results for graphs via flag algebras

Levente Bodnár, Oleg Pikhurko

The $(κ, ℓ)$ -edge-inducibility problem asks for the maximum number of $κ$ -subsets inducing exactly $ℓ$ edges that a graph of given order $n$ can have. Using flag algebras and…

math.CO2025

Turán density of tight cycles minus one edge in the $ℓ_{2}$ -norm

Levente Bodnár, Jinghua Deng, Jianfeng Hou +2

The $3$ -uniform tight $ℓ$ -cycle minus one edge $C_{ℓ}^{3 -}$ is the $3$ -graph on $ℓ$ vertices consisting of $ℓ - 1$ consecutive triples in the cyclic order. We show that f…

math.CO2025

The Turán density of short tight cycles

Levente Bodnár, Jared León, Xizhi Liu +1

The $3$ -uniform tight $ℓ$ -cycle $C_{ℓ}^{3}$ is the $3$ -graph on ${1, \dots, ℓ}$ consisting of all $ℓ$ consecutive triples in the cyclic order. Let $C$ be either…

math.CO2025

Some exact values of the inducibility and statistics constants for hypercubes

Levente Bodnár, Oleg Pikhurko

We consider two types of problems: maximising, over subsets $S \subseteq {0, 1}^{n}$ , the density of $d$ -subcubes $C$ in the $n$ -hypercube graph that span a subgraph such that $S\cap…

math.CO2024

The Turán density of the tight 5-cycle minus one edge

Levente Bodnár, Jared León, Xizhi Liu +1

Let the tight $ℓ$ -cycle minus one edge $C_{ℓ}^{3 -}$ be the $3$ -graph on ${1, \dots, ℓ}$ consisting of $ℓ - 1$ consecutive triples in the cyclic order. We show that, for eve…

cs.CC2024

CLIQUE as an AND of Polynomial-Sized Monotone Constant-Depth Circuits

Levente Bodnar

This paper shows that calculating $k$ -CLIQUE on $n$ vertex graphs, requires the AND of at least $2^{n /4 k}$ monotone, constant-depth, and polynomial-sized circuits, for sufficiently…

The quadratic Brown--Erdős--Sós problem for 3-uniform hypergraphs with 8 and 9 edges

The inducibility of 6-vertex graphs

Strong non-principality of positive codegree Turán density

On problems of Erdős and Baumann-Briggs on minimising the density of s-cliques in graphs with forbidden subgraphs

FlagAlgebraToolbox: Flag Algebra Computations in SageMath

Tetrahedron Conjecture in the ℓ2​-norm

Semi-inducibility of 4-vertex graphs

Some exact inducibility-type results for graphs via flag algebras

Turán density of tight cycles minus one edge in the ℓ2​-norm

The Turán density of short tight cycles

Some exact values of the inducibility and statistics constants for hypercubes

The Turán density of the tight 5-cycle minus one edge

CLIQUE as an AND of Polynomial-Sized Monotone Constant-Depth Circuits

On problems of Erdős and Baumann-Briggs on minimising the density of $s$ -cliques in graphs with forbidden subgraphs

Tetrahedron Conjecture in the $ℓ_{2}$ -norm

Turán density of tight cycles minus one edge in the $ℓ_{2}$ -norm