On the "solvability" of jigsaw Sudoku puzzles

Question

I am making a computer program that is going to generate Sudoku puzzles of various types. One of these types is "jigsaw", in which the board is split into rows, columns and random 9-square contiguous regions. My regions are generated completely randomly and I have become concerned that maybe there are some arrangements of region for which no solution can exist. Can anybody give me an example of this or perhaps explain why no such arrangement exists. Thank you.