Measures on monotone properties of graphs

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Abstract

Given a monotone property P of graphs, write Pn for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in Pn and the functions |Pn|. We also examine the measure eP(n), the maximum number of edges in a graph of Pn.

Keywords

Extremal graph theory
Graph properties
Monotone
Hereditary
Speed
Size.

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Research partially supported by OTKA grant F026049 and NSF Grant DMS 9971788.