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Lin-Yuan Lu

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Preprint Aug 2026

Maximum spread of $K_{s,t}$-minor-free graphs II: the non-admissible cases

We have previously determined the maximum-spread $K_{s, t}$-minor-free graph(s) on $n$ vertices when $n$ is sufficiently large, $2\le s\le t$, and $s=2$ or $t\ge \frac{3}{2}(s-3) + \frac{4}{s-1}$. In this sequel paper, we completely determine the maximum-spread $K_{s, t}$-minor-free graphs on $n$ vertices for $n$ suffi...

William Linz, Lin-Yuan Lu, Zhi-Yu Wang · 0 citations

Preprint Jul 2026

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

For a graph $G$, let $ \lambda_1(G)\ge \lambda_2(G)\ge \cdots \ge \lambda_n(G)$ denote the adjacency eigenvalues of $G$. We prove that for all looped graphs $G$ on $n$ vertices, \[\lambda_1(G) + \lambda_2(\overline{G}) \le \frac87 n. \] Our method also gives a short new proof of the Nordhaus-Gaddum result for the spect...

Sahil Agarwal, Carter Antley, Joseph Aulenbacher et al. · 1 citation · ⚡1