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.

Publication Title

Electronic Journal of Combinatorics