All Questions

It is well-known that a plane graph $G$ is Eulerian if and only if its (geometric) dual $G^*$ is bipartite. I am interested in generalisations of this result to cellular embeddings of Eulerian graphs ...

So it is well known that given a planar graph, $G$, embedded in the plane (without edge crossing, so a planar embedding). One can construct the planar dual, $G^*$. What is perhaps slightly less well-...

Given a graph the minimum genus $g$ is the minimum number of handles needed so that there an imbedding of the graph on the surface with no edge crossings. If the graph is of genus $g$ then is there ...

Given a graph $G$, there is a minimal integer $g$ associated with it which captures the minimum genus a surface needs to have so that $G$ embeds in the surface without edge crossings. Is there a way ...

In the following paper by Valiant http://www.computer.org/csdl/trans/tc/1981/02/06312176.pdf He shows under theorem 2 (at the bottom of the second page) that any planar graph $G$ of degree 3 or 4 ...