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The asymptotic numbers of certain kinds of regular toroidal maps
2000
Discrete Mathematics
The asymptotic number (of isomorphism classes) of toroidal maps of type (3; 6) with at most n vertices is found, together with the fraction of those with multiplicity 1. Accurate lower and upper asymptotic estimates are provided for the number of toroidal maps of type (3; 6) with a Hamiltonian normal cycle and with at most n vertices. The case of type (6; 3) toroidal maps follows by duality. Similar results are obtained for toroidal maps of type (4; 4). (Type (p; q)= partition into p-gons, q
doi:10.1016/s0012-365x(99)00236-8
fatcat:maiwq64nyrashcp2btsjygo4pq