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 $K_{s,t}$.
@article{10_37236_6775,
author = {Vladimir Nikiforov and Michael Tait and Craig Timmons},
title = {Degenerate {Tur\'an} problems for hereditary properties},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {4},
doi = {10.37236/6775},
zbl = {1401.05189},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6775/}
}
TY - JOUR
AU - Vladimir Nikiforov
AU - Michael Tait
AU - Craig Timmons
TI - Degenerate Turán problems for hereditary properties
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/6775/
DO - 10.37236/6775
ID - 10_37236_6775
ER -
%0 Journal Article
%A Vladimir Nikiforov
%A Michael Tait
%A Craig Timmons
%T Degenerate Turán problems for hereditary properties
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/6775/
%R 10.37236/6775
%F 10_37236_6775
Vladimir Nikiforov; Michael Tait; Craig Timmons. Degenerate Turán problems for hereditary properties. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/6775
