Orienting cycle elements in orientable rotation systems
The paper investigates, from a combinatorial point of view, the structure of the cycle space of an embedded graph. The method involves the consistent propagation of a local, initial orientation. Among others, a purely combinatorial proof of the fact that \(S(\Pi)/ N_0\) is isomorphic to the freely generated group on \(2g\) involutions, where \(g\) is the genus of the embedding \(\Pi\) with cycle space \(S(\Pi)\) and \(N_0\) is the class of \(\Pi\)-bifurcating elements of \(S(\Pi)\), is provided.
scientific article; zbMATH DE number 1121501