Document Type
Preprint
Publication Date
6-1-2022
Journal / Book Title
Graphs and Combinatorics
Abstract
The classical extremal problem is that of computing the maximum number of edges in an F-free graph. In particular, Turán’s theorem entirely resolves the case where F= Kr+1. Later results, known as supersaturation theorems, proved that in a graph containing more edges than the extremal number, there must also be many copies of Kr+1. Alon and Shikhelman introduced a broader class of extremal problems, asking for the maximum number of copies of a graph T in an F-free graph (so that T= K2 is the classical extremal number). In this paper we determine some of these generalized extremal numbers when T and F are stars or cliques and prove some supersaturation results for them.
DOI
10.1007/s00373-021-02454-y
MSU Digital Commons Citation
Cutler, Jonathan; Nir, Jd; and Radcliffe, A. J., "Supersaturation for Subgraph Counts" (2022). Department of Mathematics Faculty Scholarship and Creative Works. 253.
https://digitalcommons.montclair.edu/mathsci-facpubs/253
Rights
© The authors. Released under the CC BY-ND license (International 4.0).
Published Citation
Cutler, J., Nir, J. D., & Radcliffe, A. J. (2022). Supersaturation for subgraph counts. Graphs and Combinatorics, 38(3), 65.