Feedback arc set

This directed graph has no cycles: it is not possible to get from any vertex (point) back to that same point, following the connections in the direction indicated by the arrows.

In graph theory, a directed graph may contain directed cycles, a one-way loop of edges. In some applications, such cycles are undesirable, and we wish to eliminate them and obtain a directed acyclic graph (DAG). One way to do this is simply to drop edges from the graph to break the cycles. A feedback arc set (FAS) or feedback edge set is a set of edges which, when removed from the graph, leave a DAG. Put another way, it's a set containing at least one edge of every cycle in the graph.

单词	Feedback edge set
释义	Feedback edge set 英语百科 Feedback arc set In graph theory, a directed graph may contain directed cycles, a one-way loop of edges. In some applications, such cycles are undesirable, and we wish to eliminate them and obtain a directed acyclic graph (DAG). One way to do this is simply to drop edges from the graph to break the cycles. A feedback arc set (FAS) or feedback edge set is a set of edges which, when removed from the graph, leave a DAG. Put another way, it's a set containing at least one edge of every cycle in the graph.
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Feedback edge set

Feedback arc set