Spectral saturation: inverting the spectral Turan theorem
Combinatorics
2007-11-26 v1
Abstract
We prove that if the spectral radius of a graph G of order n is larger than the spectral radius of the r-partite Turan graph of the same order, then G contains various supergraphs of the complete graph of order r+1. In particular G contains a complete r-partite graph of size log n with one edge added to the first part. These results complete a project of Erdos from 1963. We also give corresponding stability results.
Cite
@article{arxiv.0711.3488,
title = {Spectral saturation: inverting the spectral Turan theorem},
author = {Vladimir Nikiforov},
journal= {arXiv preprint arXiv:0711.3488},
year = {2007}
}