(unweighted K node augmentation)

if any two distinct simple cycles in G have at

most one node in common (or equivalently, any link of G

belongs to at most one cycle

Let G be a finite undirected graph and x and y two distinct vertices. Then the theorem states that the size of the minimum edge cut for x and y (the minimum number of edges whose removal disconnects x and y) is equal to the maximum number of pairwise edge-independent paths from x to y.

path protection requires less capacity than

link protection, while shared protection requires less capacity

than dedicated protection. However, path protection is more

vulnerable to multiple link failures than link protection, and

so is shared protection compared to dedicated protection

The smallest capacity over all

links in the two paths is maximized.

Quality of Protection (QoP),