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Graphs that triangulate a given surface and quadrangulate another surface
AbstractWe show that for any closed surface F with χ(F)⩽−4 (or χ(F)⩽−2), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadrangulate F. We also give a sufficient condition for a graph triangulating a closed surface to quadrangulate some other surface