Back to Search
Start Over
A spectral Erdős-Rademacher theorem.
- Source :
-
Advances in Applied Mathematics . Jul2024, Vol. 158, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- A classical result of Erdős and Rademacher (1955) indicates a supersaturation phenomenon. It says that if G is a graph on n vertices with at least ⌊ n 2 / 4 ⌋ + 1 edges, then G contains at least ⌊ n / 2 ⌋ triangles. We prove a spectral version of Erdős–Rademacher's theorem. Moreover, Mubayi (2010) [28] extends the result of Erdős and Rademacher from a triangle to any color-critical graph. It is interesting to study the extension of Mubayi from a spectral perspective. However, it is not apparent to measure the increment on the spectral radius of a graph comparing to the traditional edge version (Mubayi's result). In this paper, we provide a way to measure the increment on the spectral radius of a graph and propose a spectral version on the counting problems for color-critical graphs. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SUPERSATURATION
*COUNTING
*TRIANGLES
Subjects
Details
- Language :
- English
- ISSN :
- 01968858
- Volume :
- 158
- Database :
- Academic Search Index
- Journal :
- Advances in Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 177630510
- Full Text :
- https://doi.org/10.1016/j.aam.2024.102720