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Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus
Evgeniy Krasko, Alexander Omelchenko
In this work for the first time we enumerate unlabelled maps on orientable genus surfaces with respect to all homeomorphisms, including both orientation-preserving and orientat…
Enumeration of -regular Maps on the Torus. Part II: Enumeration of Unsensed Maps
Evgeniy Krasko, Alexander Omelchenko
The second part of the paper is devoted to enumeration of -regular toroidal maps up to all homeomorphisms of the torus (unsensed maps). We describe in detail the periodic orient…
Enumeration of -regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps
Evgeniy Krasko, Alexander Omelchenko
The work that consists of two parts is devoted to the problem of enumerating unrooted -regular maps on the torus up to all its symmetries. We begin with enumerating near--reg…
Enumeration of Labelled and Unlabelled Hamiltonian Cycles in Complete -partite Graphs
Evgeniy Krasko, Igor Labutin, Alexander Omelchenko
We enumerate labelled and unlabelled Hamiltonian cycles in complete -partite graphs having exactly vertices in each part (in other words, Turán graphs $T(…