On the growth rate of minor-closed classes of graphs
نویسندگان
چکیده
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class G, we let gn be the number of graphs in G which have n vertices. A recent result of Norine et al. [12] shows that for all minor-closed class G, there is a constant c such that gn ≤ c nn!. Our main results show that the growth rate of gn is far from arbitrary. For example, no minor-closed class G has gn = c n! with 0 < c < 1 or 1 < c < ξ ≈ 1.76.
منابع مشابه
Growth constants of minor-closed classes of graphs
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class G, let gn be the number of graphs in G which have n vertices. The growth constant of G is γ = lim sup(gn/n!) . We study the properties of the set Γ of growth constants of minor-closed classes of graphs. Among other results, we show that Γ does not contai...
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