Introductory Workshop - Graph Theory: Extremal, Probabilistic and Structural: Stability of large cuts in random graphs
Presenter
February 13, 2025
Keywords:
- extremal graph theory
- random graphs
- probabilistic methods
- structural graph theory
- Ramsey theory
MSC:
- 05C35 - Extremal problems in graph theory [See also 90C35]
- 05C55 - Generalized Ramsey theory [See also 05D10]
- 05C75 - Structural characterization of families of graphs
- 05C80 - Random graphs (graph-theoretic aspects) [See also 60B20]
- 05D40 - Probabilistic methods in extremal combinatorics
- including polynomial methods (combinatorial Nullstellensatz
- etc.)
Abstract
A cut in a graph G is the set of edges that cross some partition of the vertices of G into two sets and a maximum cut of G is a cut with the largest size among all cuts. We will prove that the family of largest cuts in the binomial random graph G_{n,p} exhibits the following stability property: If 1/n