The theory of combinatorial maps and its use in the graph-topological computations.
Dainis Zeps · 1998
In this work we investigate combinatorial maps coded via permutations, applying the geometrical idea of considering the corners between the edges in the embedding of the graph on the surface to be the elements on which the permutations act. Combinatorial maps as well partial combinatorial maps are considered, theory of cycle covers, that give objects that correspond to the cycles in the graphs, are developed. Some formulae in permutations are found that calculate useful characteristics of maps. General idea of the work is to find useful applications: finding some quantities computable in permutations that has graph-theoretical characteristics in correspondence. The computer program is implemented that computes the formulae and algorithms obtained from the developed theory.