A general theorem in spectral extremal graph theory
Abstract
The extremal graphs E X ( n , F ) \mathrm {EX}(n,\mathcal F) and spectral extremal graphs S P E X ( n , F ) \mathrm {SPEX}(n,\mathcal F) are the sets of graphs on n n vertices with maximum number of edges and maximum spectral radius, respectively, with no subgraph in F \mathcal F . We prove a general theorem which allows us to characterize the spectral extremal graphs for a wide range of forbidden families F \mathcal F and implies several new and existing results. In particular, whenever E X ( n , F ) \mathrm {EX}(n,\mathcal F) contains the complete bipartite graph K k , n − k K_{k,n-k} (or certain similar graphs) then S P E X ( n , F ) \mathrm {SPEX}(n,\mathcal F) contains the same graph when n n is sufficiently large. We prove a similar theorem which relates S P E X
Fields of Study & Subjects
Graph theory and applications
Nuclear Receptors and Signaling
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 379
- Issue
- 9
- Pages
- 6535–6564
- Publication date
- 16 June 2026
- Language
- EN