A CHARACTERIZATION OF THE EMBEDDABILITY OF GRAPHS ON THE SURFACE OF GIVEN GENUS
Liuying · Acta Scientiarum Naturalium Universitatis Sunyatseni · 1996
The embedding technique based on an operator appeared in [Liu, Y. P., Scientia Sinica, Spocial Issue on Math, 1(1979), 191-201 (in Chinese)] for determining the maximum non-orientablegenus of a graph is developed to obtain the general theorem which presents a necessary andsufficient condition for a graph to be embeddable into either the orisntable or the non-orientablesurface of genus k. Furthermore, the greatest lower bound of the lengths of genus ranges of the class of nonplanar graphs which are up-embeddable is also obtained.