منابع مشابه
Some minor-closed classes of signed graphs
We define four minor-closed classes of signed graphs in terms of embeddability in the annulus, projective plane, torus, and Klein bottle. We give the full list of 20 excluded minors for the smallest class and make a conjecture about the largest class.
متن کاملAsymptotic Properties of Some Minor-Closed Classes of Graphs
Let A be a minor-closed class of labelled graphs, and let Gn be a random graph sampled uniformly from the set of n-vertex graphs of A. When n is large, what is the probability that Gn is connected? How many components does it have? How large is its biggest component? Thanks to the work of McDiarmid and his collaborators, these questions are now solved when all excluded minors are 2-connected. U...
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Given a graphH with at least one edge, let gap H (n) denote the maximum difference between the numbers of edges in two n-vertex edge-maximal graphs with no minor H . We show that for exactly four connected graphs H (with at least two vertices), the class of graphs with no minor H is pure, that is, gap H (n) = 0 for all n > 1; and for each connected graph H (with at least two vertices) we have t...
متن کاملOn the growth rate 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, 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 arbit...
متن کاملGrowth 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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.09.019