A spectral stability theorem for large forbidden graphs

TL;DR

This paper extends the spectral stability theorem to larger forbidden graphs whose size grows logarithmically with the host graph, focusing on spectral radius conditions for extremal graph properties.

Contribution

It introduces a spectral stability result for large forbidden graphs with size growing logarithmically, expanding classical stability theorems.

Findings

Spectral radius bounds characterize extremal graphs with forbidden subgraphs.

Extension of stability theorem to larger, logarithmically growing forbidden graphs.

Spectral conditions replace traditional edge-count conditions in stability analysis.

Abstract

We extend the classical stability theorem of Erdos and Simonovits in two directions: first, we allow the order of the forbidden graph to grow as log of order of the host graph, and second, our extremal condition is on the spectral radius of the host graph.