We introduce a general method to count and randomly sample unlabeled combinatorial structures. The approach is based on pointing unlabeled structures in an “unbiased” way, i.e...
Eppstein [5] characterized the minor-closed graph families for which the treewidth is bounded by a function of the diameter, which includes e.g. planar graphs. This characterizatio...
A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m ...
We present an expected polynomial time algorithm to generate an unlabeled connected cubic planar graph uniformly at random. We first consider rooted connected cubic planar graphs, ...
We present an expected polynomial time algorithm to generate a 2-connected unlabeled planar graph uniformly at random. To do this we first derive recurrence formulas to count the ...