# The fine structure of octahedron-free graphs

@article{Balogh2011TheFS, title={The fine structure of octahedron-free graphs}, author={J{\'o}zsef Balogh and B{\'e}la Bollob{\'a}s and Mikl{\'o}s Simonovits}, journal={J. Comb. Theory, Ser. B}, year={2011}, volume={101}, pages={67-84} }

This paper is one of a series of papers in which, for a family L of graphs, we describe the typical structure of graphs not containing any [email protected]?L. In this paper, we prove sharp results about the case L={O"6}, where O"6 is the graph with 6 vertices and 12 edges, given by the edges of an octahedron. Among others, we prove the following results. (a) The vertex set of almost every O"6-free graph can be partitioned into two classes of almost equal sizes, U"1 and U"2, where the graph… Expand

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