Convenient Adjacencies on $\Bbb Z^2$

Josef Šlapal

We discuss graphs with the vertex set $\Bbb Z^2$ which are subgraphs of the 8-adjacency graph and have the property that certain natural cycles in these graphs are Jordan curves, i.e., separate $\Bbb Z^2$ into exactly two connected components. After considering graphs with the usual connectedness, we concentrate on a graph with a special one.