Surface triangulations without short noncontractible cycles
Teresa M. Przytycka, Józef H. Przytycki · Contemporary mathematics - American Mathematical Society · 1993
. We discuss three methods of constructing surface triangulations that do not have short noncontractible cycles (equivalently, that have high representativity). The three methods are: the covering spaces technique, a combinatorial method, and a method that applies hyperbolic geometry. Using the first method we show that for any genus g and n c 1 g log log g there exists a triangulation of a genus g surface with an n vertex graph such that the representativity is at least c 0 1 p n=g p log log g (where c 1 ; c 0 1 are constants) . Using the second method we show that for any genus g and n ? c 2 g log g there exists a triangulation of a genus g surface with an n vertex graph such that the representativity is at least c 0 2 p n=g p log g (where c 2 ; c 0 2 are constants). Finally, the third method allows us to develop an argument which leads to the conjecture that, for any g and n sufficiently large, a surface of genus g can be triangulated with representativity at least...