Quotients of connected regular graphs of even degree (Q1063616)

A powerful technique for imbedding graphs on surfaces constructs a desired imbedding as a (possibly branched) covering space over a simpler imbedding (of a voltage graph). Thus it is useful to determine quotients of a given graph; these are candidates for a suitable voltage graph. \textit{J. L. Gross} and \textit{T. W. Tucker} [Pac. J. Math. 55, 391-402 (1974; Zbl 0306.55001)] described all regular quotients of complete graphs. The present paper introduces a method for describing all quotients (both regular and irregular) of finite connected regular graphs of even degree, with a given 2-factorization. This method is based on the characterization by \textit{J. L. Gross} [J. Comb. Theory, Ser. B 22, 227- 232 (1977; Zbl 0369.05042)] of finite Schreier coset graphs as regular graphs of even degree.