2013/12/19 by Hamed Hatami, Svante Janson, Hatami, Hamed +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · doi:10.48550/arxiv.1312.5626
openalex publication_date 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the relation between the growth rate of a graph property and the entropy of the graph limits that arise from graphs with that property. In particular, for hereditary classes we obtain a new description of the colouring number, which by well-known results describes the rate of growth. We study also random graphs and their entropies. We show, for example, that if a hereditary property has a unique limiting graphon with maximal entropy, then a random graph with this property, selected uniformly at random from all such graphs with a given order, converges to this maximizing graphon as the order tends to infinity.