In this paper, we use constructions of Heffter arrays to verify the existence of face 2‐
colorable embeddings of cycle decompositions of the complete graph. Specifically, for n≡ 1 …

We give a more simple proof of the Map Color Theorem for nonorientable surfaces that uses
only four constructions of current graphs instead of 12 constructions used in the previous …

We show that the number of nonisomorphic (both orientable and nonorientable) triangular
embeddings of $ K_n $, $ n\equiv 0$ or $1\pmod {3} $, $ n\geq 6$, is less than the number …

Until recently there were no results on the orientable or nonorientable genus of graphs K n+
K m¯ for n/2≤ m< n− 1. Recently, using index one current graphs, McCourt (2014) …