Surface embedding of graphs
Yan Liu · 2003
This paper provided polygonal representation of surfaces.Although it was evaluated from polyhedral representation, many problems, e.g.,the existance and enumeration of graphs on surfaces, the determination of the maximjum genus of a graph could be solved much simpler in this way. Polyhedral representation was initiated by Heffter.Hilbert and CohnVossen posed the thread problem and had it related to the Heawood map color conjecture.The conjecture was not proved until Ringel et al.Edmonds(1960) polyhedral representation used to be cited very often for about three decades until it was found that Edmonds′ was the dual of Heffter′s.Polygonal representation began to appear first in the author′s monographs.However, its powerfullness had not been uncovered until this paper come out which was seen as a bridge to the combinatorial map theory.