Spectral saturation: Inverting the spectral Turán theorem
Let μ(G) be the largest eigenvalue of a graph G and Tr (n) be the r-partite Turán graph of order n. We prove that if G is a graph of order n with μ (G) > μ(Tr. (n)), then G contains various large supergraphs of the complete graph of order r + 1, e.g., the complete r-partite graph with all parts of size log'n with an edge added to the first part. We also give corresponding stability results.
Electronic Journal of Combinatorics
Nikiforov, V. (2009). Spectral saturation: Inverting the spectral Turán theorem. Electronic Journal of Combinatorics, 16 (1) https://doi.org/10.37236/122