Author

Ruilin Zheng

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Preprint Sep 2026

The diameter of recoloring graphs under a maximum average degree bound

For a graph $G$, we write $\mathrm{mad}(G)$ for its maximum average degree and $\mathrm{diam} G$ for its diameter. Let $R_k(G)$ be the graph whose vertices are the proper colorings of $G$ with $k$ colors, where two colorings are adjacent when they differ at one vertex. Feghali (JCTB, 2021) proved that, for fixed intege...

Rui-Lin Zheng, Jun-Ying Lu · 0 citations

Preprint Aug 2026

Clique-saturating non-edges throughout the Tur\'an range

For an $F$-free graph $G$, a non-edge is $F$-saturating if adding it to $G$ creates a copy of $F$. We denote by $f_{p+1}(n,m)$ the minimum number of $K_{p+1}$-saturating non-edges in a $K_{p+1}$-free $n$-vertex graph with $m$ edges. Erd\H{o}s and Tuza conjectured that $f_4\left(n,\mathrm{ex}(n,K_3)+ 1\right)= (1 + o(1)...

Xiaolin Wang, Jiabao Yang, Rui-Lin Zheng · 0 citations