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Vladimir Nikiforov
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Michael Tait
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Craig Timmons
Keywords:
Turán problem, Hereditary property, Spectral radius
Abstract
Let $H$ be a graph and $t\geqslant s\geqslant 2$ be integers. We prove that if $G$ is an $n$-vertex graph with no copy of $H$ and no induced copy of $K_{s,t}$, then $\lambda(G) = O\left(n^{1-1/s}\right)$ where $\lambda(G)$ is the spectral radius of the adjacency matrix of $G$. Our results are motivated by results of Babai, Guiduli, and Nikiforov bounding the maximum spectral radius of a graph with no copy (not necessarily induced) of $K_{s,t}$.