Peripheral cycle

Peripheral cycle

In graph theory, a peripheral cycle in a graph "G" is a cycle that is induced and "non-separating". That is, it is a cycle "C" such that
* no two vertices in "C" are connected by an edge not in "C" and
* the graph "G" − "C" (we are deleting vertices of "C" and all incident edges) is connected.

Properties

In a 3-connected planar graph, boundaries of facesare precisely the peripheral cycles.

The cycle space of a 3-connected graph is generated by the peripheral cycles (a result of Tutte, 1963).

External links

* Reinhard Diestel: [http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/ Graph Theory]


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