A simple cycle is peripheral if it has exactly one bridge.

We can use the tools we have here to make a simple automatic cycle.

Any connected graph without simple cycles is a tree.

An example would be finding a simple cycle of length in graph .

Therefore, it takes overall time to find a simple cycle of length in .

Equivalently, every edge in such a graph belongs to at most one simple cycle.

In other words, any connected graph without simple cycles is a tree.

G has no simple cycles and has n 1 edges.

Upon this rich food It existed in a simple cycle of waking to eat and sleeping to dream.

In the contracted graph, generally stops being a simple cycle and becomes instead an Euler tour.