We show that for n= 4 and n⩾ 6, Kn has a nonorientable embedding in which all the facial
walks are hamilton cycles. Moreover, when n is odd there is such an embedding that is 2 …

We construct several families of minimum genus embeddings of dense graphs using index 2
current graphs. In particular, we complete the genus formula for the octahedral graphs …

Abstract Let $\kappa_ {max}(\Sigma) $ denote the maximum value for the connectivity of any
graph which embeds in the topological surface $\Sigma $. The connectivity interval for …

In 1972, Kainen proved a general lower bound on the crossing number of a graph in a
closed surface and conjectured that this bound is tight when the graph is either a complete …

We construct several families of minimum genus embeddings of dense graphs using index 2
current graphs. In particular, we complete the genus formula for the octahedral graphs …