Shumin Sun

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5 papers · 1 filter

math.CO2026

The inducibility of 6-vertex graphs

Levente BodnÃ¡r, Jun Gao, Jared LeÃ³n +3

The inducibility constant $I^»_{F}$ of a graph $F$ is the asymptotically maximum induced density of $F$ in a growing sequence of graphs. This paper systematically investigates the c…

math.CO2026

Strong non-principality of positive codegree TurÃ¡n density

Levente BodnÃ¡r, Jun Gao, Oleg Pikhurko +2

The \emph{minimum positive codegree} $I^´_{k - 1}^{+} (G)$ 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…

math.CO2026

Rational codegree TurÃ¡n density of hypergraphs

Jun Gao, Oleg Pikhurko, Mingyuan Rong +1

Let $H$ be a $k$ -graph (i.e. a $k$ -uniform hypergraph). Its minimum codegree $I^´_{k - 1} (H)$ is the largest integer $t$ such that every $(k - 1)$ -subset of $V (H)$ is contained in at le…

math.CO2025

Covering large-dimensional Euclidean spaces by random translates of a given convex body

Boris Bukh, Jun Gao, Xizhi Liu +2

Determining the minimum density of a covering of $R^{n}$ by Euclidean unit balls as $n \to \infty$ is a major open problem, with the best known results being the lower bound…

math.CO2025

On the quadratic 8-edge case of the Brown-ErdÅs-SÃ³s problem

Oleg Pikhurko, Shumin Sun

Let $f^{(r)} (n; s, k)$ be the maximum number of edges in an $n$ -vertex $r$ -uniform hypergraph containing no $k$ edges on at most $s$ vertices. Brown, ErdÅs and SÃ³s conjectured in 1…

The inducibility of 6-vertex graphs

Strong non-principality of positive codegree TurÃ¡n density

Rational codegree TurÃ¡n density of hypergraphs

Covering large-dimensional Euclidean spaces by random translates of a given convex body

On the quadratic 8-edge case of the Brown-ErdÅs-SÃ³s problem

On the quadratic 8-edge case of the Brown-ErdÅs-SÃ³s problem