Author

Pei Liu

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Preprint Sep 2026

The maximum spectral radius of uniform hypergraphs whose shadow excludes a complete or complete bipartite minor

For a $k$-uniform hypergraph $\mathcal H$, the shadow of $\mathcal H$ is the graph whose edges are the pairs covered by a hyperedge. In this paper, for all sufficiently large $n$, we determine the $n$-vertex $k$-uniform hypergraphs of maximum adjacency-tensor spectral radius whose shadow has no $K_t$ minor, for every $...

Pei Liu, O. Suil · 0 citations

Preprint Jul 2026

A sharp Randi\'c bound for K\"onig--Egerv\'ary graphs and a conjecture of Aouchiche, Hansen, and Zheng

Let $\alpha'(G)$ be the matching number of a graph $G$, and let its Randi\'c index be $R(G)=\sum_{uv\in E(G)}(d(u)d(v))^{-1/2}$. In 2006, Aouchiche, Hansen, and Zheng conjectured that the maximum of $R(G)-\alpha'(G)$ over all $n$-vertex graphs is attained by the complete bipartite graph whose smaller part has $\lfloor\...

Pei Liu, F. Nan, O. Suil et al. · 0 citations