Journal of Combinatorial Theory Series B
Linear time low tree-width partitions and algorithmic consequences
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proper minor-closed families are small
Journal of Combinatorial Theory Series B
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
Grad and classes with bounded expansion II. Algorithmic aspects
European Journal of Combinatorics
Grad and classes with bounded expansion III. Restricted graph homomorphism dualities
European Journal of Combinatorics
A separator theorem for string graphs and its applications
Combinatorics, Probability and Computing
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A class of simple undirected graphs is small if it contains at most n!@a^n labeled graphs with n vertices, for some constant @a. We prove that for any constants c,@e0, the class of graphs with expansion bounded by the function f(r)=c^r^^^1^^^/^^^3^^^-^^^@e is small. Also, we show that the class of graphs with expansion bounded by 6@?3^r^l^o^g^(^r^+^e^) is not small.