Spectral saturation: inverting the spectral Turan theorem

Details Spectral saturation: inverting the spectral Turan theorem Spectral saturation: inverting the spectral Turan theorem

2007-11-22

arxiv.org/abs/0711.3488v1

Mathematics

Combinatorics

Scientific paper

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.

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