In interval scheduling, the algorithm is to pick the earliest finish time. But in interval colouring the former does not work. Is there an example or explanation on why picking earliest finish time...

How to calculate the ways to paint a tree's nodes with m colors so that the ends of each edge have different colors? Any polynomial solution is welcome.

Consider a n * n binary matrix. Each cell of this matrix has at most 4 neighbors (if it exists). We call two cells of this matrix incompatible if they are neighbors and their values are not equal. ...