Regular homomorphisms and regular maps

Authors:
Aleksander Malnič;Roman Nedela;Martin Škoviera
Affiliations:
Pedagoska Fakulteta, Univerza v Ljubljani, Kardeljeva pl. 16, 1000 Ljubljana, Slovenia;Fakulta Financií, Univerzita Mateja Bela, SK-975 49 Banská Bystrica, Slovakia;Matematicko-fyzikálna Fakulta, Univerzita Komenského, SK-842 15 Bratislava, Slovakia
Venue:
European Journal of Combinatorics
Year:
2002

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Abstract

Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. Lifting and projecting groups of automorphisms along regular homomorphisms is studied in some detail. Finally, the split-extension structure of lifted groups is analysed.