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arXiv · 1312.5626

Graph properties, graph limits and entropy

Hamed Hatami·Svante Janson·Balázs Szegedy
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Abstract

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.

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Hamed Hatami, Svante Janson, Balázs Szegedy. 2013-12-19. Graph properties, graph limits and entropy. https://arxiv.org/abs/1312.5626

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