Genus distributions for two classes of graphs

Furst, Merrick L.; Gross, Jonathan L.; Statman, Richard

The set of orientable imbeddings of a graph can be partitioned according to the genus of the imbedding surfaces. A genus-respecting breakdown of the number of orientable imbeddings is obtained for every graph in each of two infinite classes. It is proved that the genus distribution of any member of either class is strongly unimodal. These are the first two infinite classes of graphs for which such calculations have been achieved, except for a few classes, such as trees and cycles, whose members have all their cellular orientable imbeddings in the sphere.



More About This Work

Academic Units
Computer Science
Department of Computer Science, Columbia University
Columbia University Computer Science Technical Reports, CUCS-296-87
Published Here
December 2, 2011