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    Counting unlabelled toroidal graphs with no K33-subdivisions

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    We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of core graphs. Using structure theorems for toroidal and projective-planar graphs containing no K33-subdivisions, we apply these techniques to obtain their unlabelled enumeration.Comment: 25 pages (some corrections), 4 figures (one figure added), 3 table
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