Constructing regular maps and graphs from planar quotients
Stanislav Jendrol′, Roman Nedela, Martin Škoviera · Czech digital mathematics library · 1997
Let M be a map on an orientable surface.The generic regular map for M is, up to isomorphism, the unique regular map M# such that M# covers M and every regular map that covers M covers also M#.In this paper, we show that several interesting results concerning maps on surfaces and graphs can be established by constructing generic maps over appropriate quotients.Among them are simple proofs of theorems ofVince, MacBeath, and generalizations of results of Brown and Connelly, Archdeacon, and others.Using the same method we also show that for every integer g > 3 there exists an arctransitive cubic graph whose girth equals g.