Peripheral cycle

In this graph, the red triangle formed by vertices 1, 2, and 5 is a peripheral cycle: the four remaining edges form a single bridge. However, pentagon 1–2–3–4–5 is not peripheral, as the two remaining edges form two separate bridges.

In graph theory, a peripheral cycle (or peripheral circuit) in an undirected graph is, intuitively, a cycle that does not separate any part of the graph from any other part. Peripheral cycles (or, as they were initially called, peripheral polygons, because Tutte called cycles "polygons") were first studied by Tutte (1963), and play important roles in the characterization of planar graphs and in generating the cycle spaces of nonplanar graphs.[1]

  1. ^ Tutte, W. T. (1963), "How to draw a graph", Proceedings of the London Mathematical Society, Third Series, 13: 743–767, doi:10.1112/plms/s3-13.1.743, MR 0158387.