Regular colored graphs of positive degree

Understand

Regular colored graphs are dual representations of pure colored D-dimensional complexes.

• These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus.
• We analyse the structure of regular colored graphs of fixed positive degree and perform their exact and asymptotic enumeration.
• In particular we show that the generating function of the family of graphs of fixed degree is an algebraic series with a positive radius of convergence, independant of the degree.