I am interested in a certain class of graphs but have very little graph theory background, I was hoping that you guys could poke me in the right direction. The class of graphs is as follows:
- Connected components are directed Euler graphs
- Minimal degree is $4$
- We are given an embedding in $X$, a compact orientable surface of genus $g$.
- The faces of the graph (when considering said embedding) are $4$-colourable.
I'm interested in any property of these graphs!
Thanks in advance!