A lower ideal is a class of graphs closed under isomorphism and taking minors, and it is called proper if it is not the class of all graphs. We say that a class C of graphs is small if there exists a constant c such that the number of graphs in C with vertex-set [n] := {1, 2,...,n} is at most n!
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 !
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 ...
Oct 22, 2024 · The proper minor-closed classes (including the classes of bounded treewidth) are small, i.e., in each such class the number of labeled n-vertex ...
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 ...
Proper minor-closed families are small (with P. Seymour, R. Thomas and P. Wollan), J. Comb. Theory B 96 (2006), 754-757. New tools and results in graph minor ...
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-.
Each (proper) minor-closed graph class 𝒜 is small. We can prove this using Mader's result that each graph in 𝒜 has average degree at most b. Colin ...
[PDF] Proper Minor-Closed Classes of Graphs have Assouad–Nagata ...
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So let's consider when we can force it to be small. A dilation is a function ... Any class that is not contained within a proper minor-closed class and is closed.
Jan 13, 2012 · For any integer k, the graphs with treewidth at most k define a minor-closed family. At first the idea of the proof doesn't seem to be ...