One of the phenomena associated with self-avoiding walks and statistical physics models in general is the notion of universality, that is, independence of macroscopic observables from microscopic details, such as the choice of the lattice. One important quantity that appears in conjectures for universal laws is the connective constant, defined as follows. Let c n denote the number of n -step self-avoiding walks. Since every (n + m) -step self avoiding walk can be decomposed into an n -step self-avoiding walk and an m -step self-avoiding walk, it follows that c n + m ≤ c n c m. Therefore, the sequence {log c n } is subadditive and we can apply Fekete's lemma to show that the following limit exists: