Graph Colouring Instructions

Here is a classic graph theory problem: Put numbers (or "colours") 1, 2, or 3 into each circle so that adjacent circles receive different numbers. I guess some puzzles may use more colours, and that will be indicated for each puzzle.

Here is a simple example:

Notice that the circle on the top is adjacent to circles already coloured 1 and 2. So that circle must be coloured with 3. Then the circle on the right must be coloured with 1. So the solution for this puzzle is
.