2013/05/16 by Hamed Hatami, HAMED HATAMI, Serguei Norine +1 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph theory and applications #Limits and Structures in Graph Theory
paper · doi:10.1017/s0963548313000175
openalex publication_date 2013/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Every graphon defines a random graph on any given number n of vertices. It was known that the graphon is random-free if and only if the entropy of this random graph is subquadratic. We prove that for random-free graphons, this entropy can grow as fast as any subquadratic function. However, if the graphon belongs to the closure of a random-free hereditary graph property, then the entropy is O ( n log n ). We also give a simple construction of a non-step-function random-free graphon for which this entropy is linear, refuting a conjecture of Janson.