Related Concepts
Peripheral cycles have also been called non-separating cycles, but this term is ambiguous, as it has also been used for two related but distinct concepts: simple cycles the removal of which would disconnect the remaining graph, and cycles of a topologically embedded graph such that cutting along the cycle would not disconnect the surface on which the graph is embedded.
In matroids, a non-separating circuit is a circuit of the matroid (that is, a minimal dependent set) such that deleting the circuit leaves a smaller matroid that is connected (that is, that cannot be written as a direct sum of matroids). These are analogous to peripheral cycles, but not the same even in graphic matroids (the matroids whose circuits are the simple cycles of a graph). For example, in the complete bipartite graph, every cycle is peripheral (it has only one bridge, a two-edge path) but the graphic matroid formed by this bridge is not connected, so no circuit of the graphic matroid of is non-separating.
Read more about this topic: Peripheral Cycle
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