Abstract :
Tutteʹs description of the (di)chromatic polynomial of a graph in terms of activities with respect to maximal forests gives rise to a partition of the power-set of the edge-set as a collection of intervals, one corresponding to each maximal forest. This partition is useful in producing simplified expressions of all-terminal reliability. We compare two similar partitions connected with K-terminal reliability, one due to the author and the other due to Colbourn and Pulleyblank.
