Author

Michael Tait

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Preprint Oct 2026

Clique and chromatic numbers of graph powers: spectral bounds and anticodes

Using spectral and polynomial methods, we show several sharp spectral bounds for the clique and chromatic numbers of graph powers that only use spectral information from the original graph. In particular, we strengthen earlier spectral-radius estimates to obtain an asymptotically sharp colouring bound for general graph...

A. Abiad, Gabriel Coutinho, Hitesh Kumar et al. · 0 citations

Preprint Sep 2026

Connected graphs with minimum adjacency spectral gap

Let $G$ be a connected graph, and let $\lambda_1(G)>\lambda_2(G)$ denote its two largest adjacency eigenvalues. The spectral gap of $G$ is defined as the difference $\lambda_1(G) - \lambda_2(G)$. For integers $r\geq 2$ and $s\geq 0$, the double kite $DK(r,s)$ is formed by taking two vertex-disjoint copies of the comple...

Le-Le Liu, Michael Tait, Yi Wang · 0 citations