On the entropy of hereditary classes of colored graphs

The results obtained earlier for hereditary classes of ordinary graphs are generalised to hereditary classes of coloured graphs. A coloured graph is a complete ordinary graph with coloured edges. We prove that the smallest positive value of the entropy of hereditary classes of $q$-coloured graphs is equal to $(1/2)\log_q2$ and characterise the minimal classes with such value of the entropy.
The research was supported by the Russian Foundation for Basic Research, grant 98–01–00792.