A triangulation of a surface is called a Fisk triangulation if the degree of all but two vertices is even, and these two exceptional vertices of odd degree are neighbors.
I would like to know what conditions must be satisfied by the degree sequence of such graphs.
I've found several results about the degree sequences of *general* triangulations of surfaces, but nothing about Fisk triangulations.
Can we, for example, have that every even degree equals 6?



Eberhard-type theorems for Fisk triangulations?
Günter Rote has just shown me a (5,6,..,6,7) triangulation of the Klein-bottle where 5 and 7 are neighbors. He has also found several similar higher genus triangulations.


