In 2015 I started implementing the 1979 algorithm by Lipton and Tarjan for partitioning a planar graph. This theorem has been used to theoretically solve hundreds of other problems. However, at the time of graduation I was only 90% complete it, and have been busy with other projects to work on the other 90%. I’m hoping it can be included in the Boost Graph Library someday. If this is something you’d like to see completed or could help out with, let me know.
I started this project after looking for the most complicated algorithms in computer science and came across Bernard Chazelle’s paper for triangluating a polygon in linear time: https://www.cs.princeton.edu/~chazelle/pubs/polygon-triang.pdf I quickly realized the whole algorithm would take years to implement and would only be faster for polygons with an astronomically large number of edges. The Lipton-Tarjan algorithm is used as a subroutine.