A necessary and sufficient condition for lower bounds on crossing numbers of generalized periodic graphs in an arbitrary surface

Xiwu Yang, Xiaodong Cheng, Yuansheng Yang

Let $H$, $T$ and $C_n$ be a graph, a tree and a cycle of order $n$, respectively. Let $H^{(i)}$ be the complete join of $H$ and an empty graph on $i$ vertices. Then the Cartesian p…