Runze Wang

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8 papers · 1 filter

math.CO2025

Strong hub cover pebbling number

Runze Wang

In a graph $G$ , we define a set of vertices to be a \emph{strong hub set} if for any two vertices in $G$ , we can find a path between them whose internal vertices are all in this se…

math.CO2025

On Relative Ordered Turán Density

Dylan King, Bernard Lidický, Minghui Ouyang +3

For an ordered graph $F$ , denote the Turán density by $π (F)$ . The relative Turán density, denoted by $ρ (F)$ , is the supremum over $α \in [0, 1]$ such that every ordered graph $G$ …

math.CO2025

Discrete isoperimetric inequalities on the strong products of paths

Runze Wang

For a graph $G = (V, E)$ and a nonempty set $S \subseteq V$ , the \emph{vertex boundary} of $S$ , denoted by $\partial_{G} (S)$ , is defined to be the set of vertices that are not in $S$ b…

math.CO2024

Graph identification index

Runze Wang

We introduce the \emph{ID-index} of a finite simple connected graph. For a graph $G = (V, E)$ with diameter $d$ , we let $f : V ⟶ R$ assign \emph{ranks} to the ve…

math.CO2024

New developments on graph sum index

Dheer Noal Desai, Runze Wang

In a graph, we assign distinct integers to the vertices, and take the sum of two integers if they are on two adjacent vertices. The minimum possible number of different sums is the…

math.CO2024

On the size of sets avoiding a general structure

Runze Wang

Given a finite abelian group $G$ and a subset $S \subseteq G$ , we let $N_{G, S}$ be the smallest integer $N$ such that for any subset $A \subseteq G$ with $N$ elements, we have $g+S…

math.CO2024

A note on the threshold numbers of cycles

Runze Wang

A graph $G = (V, E)$ is said to be a \textit{ $k$ -threshold graph} with \textit{thresholds} $θ_{1} < θ_{2} < ... < θ_{k}$ if there is a map $r : V ⟶ R$ such that $uv \in E$ if…

math.CO2024

Threshold numbers of some graphs

Runze Wang

A graph $G = (V, E)$ is called a \emph{ $k$ -threshold graph} with \emph{thresholds} $θ_{1} < θ_{2} < ... < θ_{k}$ if we can assign a real number $r (v)$ to each vertex $v \in V$ , such that for any $…