This isn&#x27;t a big theorem - to some extent it&#x27;s just a trivial observation.  But it is a gateway into talking about graph theory.<p>Why should it be that a doodle is always two-colorable?  It&#x27;s a question a child could ask, but it leads to the whole area of graph theory.  Personally, I find it a much better introduction to Graph Theory than the usual question about the Bridges of Königsberg:<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Seven_Bridges_of_Königsberg" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Seven_Bridges_of_Königsberg</a><p>But there is a progression.<p>* A doodle is two-colorable<p>* A doodle is a planar, connected, Eulerian graph<p>* The dual of a planar, connected, Eulerian graph is bi-partite<p>* Bi-partite graphs are trivial to identify, and trivial to colour.<p>* What about tri-partite graphs?<p>* Identifying whether a given graph is tri-partite is NP-Complete.