A two-pieces "country" on a plane makes the map coloring problem equivalent to coloring a map on a torus.
<a href="//commons.wikimedia.org/wiki/User:Mrmw" title="User:Mrmw">Mrmw</a>
2021-03-02
Own work based on: <a href="//commons.wikimedia.org/wiki/File:4CT_Inadequacy_Explanation.png" title="File:4CT Inadequacy Explanation.png">4CT Inadequacy Explanation.png</a>: <a href="//commons.wikimedia.org/wiki/File:4CT_Inadequacy_Explanation.png" class="image"><img alt="4CT Inadequacy Explanation.png" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/97/4CT_Inadequacy_Explanation.png/80px-4CT_Inadequacy_Explanation.png" decoding="async" width="80" height="41" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/9/97/4CT_Inadequacy_Explanation.png/120px-4CT_Inadequacy_Explanation.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/9/97/4CT_Inadequacy_Explanation.png/160px-4CT_Inadequacy_Explanation.png 2x" data-file-width="468" data-file-height="237"></a>