Author

Wenqian Zhang

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Preprint Aug 2026

Extremal graphs for disjoint union of stars and paths

Let $F$ be a graph. A graph $G$ is called $F$-free if $G$ does not contain $F$ as a subgraph. Let ${\rm EX}(n,F)$ denote the set of $F$-free graphs of order $n$ with the maximum edges. In this paper, we characterize the graphs in ${\rm EX}(n,F)$ for large $n$, where $F$ is the disjoint union of paths and stars. This ge...

Wenqian Zhang · 0 citations

Preprint Aug 2026

The toughness of random graphs

For a connected and non-complete graph $G$ of order $n$, its toughness is defined as \[ \tau(G)=\min\bigl\{|S|/c(G-S):S\subseteq V(G),\ c(G-S)>1\bigr\}, \] where $c(G-S)$ denotes the number of components of $G-S$. Let $\alpha(G)$ denote the independence number of $G$. An elementary bound on toughness is $$\tau(G)\leq\f...

Guang Li, Wenqian Zhang · 0 citations