Degenerate Turán problems for hereditary properties
Let H be a graph and t ≥ s ≥ 2 be integers. We prove that if G is an n-vertex graph with no copy of H and no induced copy of Ks,t, then λ(G) = O(n1-1/s) where λ(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 Ks,t.
Electronic Journal of Combinatorics
Nikiforov, V., Tait, M., & Timmons, C. (2018). Degenerate Turán problems for hereditary properties. Electronic Journal of Combinatorics, 25 (4) https://doi.org/10.37236/6775