Large Deviation Principles for Block and Step Graphon Random Graph Models

no code implementations • 18 Jan 2021 • Jan Grebík, Oleg Pikhurko

Borgs, Chayes, Gaudio, Petti and Sen [arXiv:2007. 14508] proved a large deviation principle for block model random graphs with rational block ratios.

Graph Sampling Probability Combinatorics 05C80, 60F10

Stability from graph symmetrisation arguments with applications to inducibility

no code implementations • 19 Dec 2020 • Hong Liu, Oleg Pikhurko, Maryam Sharifzadeh, Katherine Staden

We present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation.

Combinatorics