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The early evolution of the H-free process

Abstract:

The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subject to the constraint that no H subgraph is formed. Let G be the random maximal H-free graph obtained at the end of the process. When H is strictly 2-balanced, we show that for some c>0, with high probability as $n \to \infty$, the minimum degree in G is at least $cn^{1-(v_H-2)/(e_H-1)}(\log n)^{1/(...

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Publisher copy:
10.1007/s00222-010-0247-x

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
Inventiones Mathematicae
Volume:
181
Issue:
2
Pages:
291-336
Publication date:
2009-08-04
DOI:
EISSN:
1432-1297
ISSN:
0020-9910
URN:
uuid:5bff9302-49c0-49ac-aad5-077d4eb3f0bc
Source identifiers:
430652
Local pid:
pubs:430652
Language:
English
Keywords:

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