The utility of a Kolmogorov complexity method in combinatorial theory is demonstrated by several examples.

We study partitions of Fra¨ıssé limits of classes of finite relational structures where the partitions are encoded by infinite binary strings which are random in the sense of Kolmogorov-Chaitin.

We consider stochastically modeled reaction networks and prove that if a constant solution to the Kolmogorov forward equation decays fast enough relative to the transition rates, then the model is non-explosive. In particular, complex balanced reaction networks are non-explosive.

We present a brief survey of results on relations between the Kolmogorov complexity of infinite strings and several measures of information content (dimensions) known from dimension theory, information theory or fractal geometry. Special emphasis is laid on bounds on the complexity of strings in constructively given subsets of the Cantor space. Finally, we compare the Kolmogorov complexity to t...