Author

Bo Ning

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Preprint Sep 2026

Longest cycles intersect linearly in highly connected graphs

A longstanding conjecture attributed to Smith (1984) asserts that for every $k\ge2$, any two longest cycles in a $k$-connected graph share at least $k$ vertices. In this paper, we prove the first linear lower bound, showing that any two longest cycles in a $k$-connected graph share at least $k/600$ vertices. Departing...

Jie Ma, Bo Ning, Zi-Yuan Zhao · 0 citations

Review Aug 2026

On the difference between clique partition and clique covering numbers of graphs

For a graph $G$, let $\cpn(G)$ and $\ccn(G)$ denote the minimum numbers of cliques whose edge sets partition and cover $E(G)$, respectively, and put $f(n)=\max_{|V(G)|=n}\bigl(\cpn(G)-\ccn(G)\bigr).$ In 1983, Erd\H{o}s, Faudree, and Ordman asked whether there is a sequence of graphs $G_n$ such that $|V(G_n)|=n$ and $\c...

Bo Ning · 0 citations