As a kid, I shared the dreams of many: to become a Pokemon master. Although I can’t say I ever achieved this goal (because they keep making hundreds of new ones every year), one thought that came to mind after today’s class was the many routes in each region of the game that connect cities and towns to more cities and towns.
As the games have progressed, we’ve seen a drastic improvement in the overall layout of each region. Here below is the Kanto Region, in all of its glory:
And now, a map of the Kalos region, in a game released around twenty years later:
There are seven regions to choose from in the mainstream games, but personally I found that Kalos has a beautiful array of plots and lines to analyze.
Below is a more linear image of Kalos from Serebii.net, where you can see clear paths from one destination to the next. In math terms, a blue or orange dot represent the vertices here, and the white routes are edges:
Now for the big question: Is there a Euler’s Circuit or path in this Pokemon region? Unfortunately the answer is no, I found at least four or five odd degree vertices here. On another note, I couldn’t find a Pokemon region that was fully connected (that is, because there are often islands within the game for players to sail to).
The region which I believe does contain a Euler’s Path would be Generation V’s Unova, which as you can see below should have (if my counting is correct) exactly two odd vertices:
Did you guys find this post interesting? Am I off regarding how graphing theory works? Let me know in the comments below! Thought it’d be cool to reference one of the greatest series of RPGs out there.
Sources: https://bulbapedia.bulbagarden.net/wiki/File:Unova.png, https://imgur.com/r/all/kCiUIuE, https://www.serebii.net/pokearth/kalos/, https://bulbapedia.bulbagarden.net/wiki/File:Kanto_Town_Map_RBY.png