Divide the grid in N regions of different sizes between 1 and N. All the vertices where 3 borders of regions meet are given. There are no vertices where 4 borders meet.
(Rules (modified) and example (N = 5) from WPC 2018 IB)
History of the puzzle
Invented by Yukari Nishiyama (Japan) in 2001. First appeared as a submission to Internet Gekisakujuku, a contest where the best new puzzle type was decided from types submitted by readers of Puzzler magazine.  Originally titled 1から8分割 (Dissection from 1 to 8). As the name suggests, N was always 8 and the grid was always 6x6.
The name of this article is based on a puzzle from WPC 2012/Part 8.