Proper minor-closed families are small

Authors:
Serguei Norine;Paul Seymour;Robin Thomas;Paul Wollan
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA;Department of Mathematics, Princeton University, Princeton, NJ;School of Mathematics, Georgia Institute of Technology, Atlanta, GA;School of Mathematics, Georgia Institute of Technology, Atlanta, GA
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

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Abstract

We prove that for every proper minor-closed class I of graphs there exists a constant c such that for every integer n the class I includes at most n!cn graphs with vertex-set {1, 2,...,n}. This answers a question of Welsh.