Given a cycle of length > 3 in a planar graph, I'm looking to partition it into 4 sublists of length 2 or more such that:
- No sublist contains two vertices with a chord between them
- The last element in each sublist is the first element in the next
- Every element in each sublist is adjacent to its neighbors in the original cycle
- The difference in size between the sublists is kept minimal, given constraints 1 to 3
Overall I'm not really sure if this is required to be solved using graph structures, or if it's possible to transform it into something more general.