Branched coverings of graph imbeddings
Jonathan L. Gross, Seth R. Alpert · Bulletin of the American Mathematical Society · 1973
This announcement outlines a reformulation of W. Gustin's combinatorial theory of current graphs [3] and J. W. T. Youngs' extension of that theory to vortex graphs [8] into the topological context of covering spaces and branched covering spaces.Whereas certain restrictions imposed by Gustin and Youngs were convenient in obtaining minimal imbeddings of complete graphs, leading to the solution of the Heawood map-coloring problem (see Ringel and Youngs [6]), the present relaxation of those restrictions leads to a more general method of constructing minimal and other imbeddings of graphs.