A sharp spectral extremal result for general non-bipartite graphs

Paper

Abstract

For a graph family

, let

and

denote the maximum number of edges and maximum spectral radius of an

-vertex

-free graph, respectively, and let

and

denote the corresponding sets of extremal graphs. Wang, Kang, and Xue showed that if

and

then

for

large enough. Fang, Tait, and Zhai extended this result by showing if

then

for

large enough, and asked for the maximum constant

such that

guarantees such containment. In this paper we determine

exactly for all