circuit rank

In both cases the number of ears is necessarily equal to the circuit rank of the given graph.

The corank of the graphic matroid is known as the circuit rank or cyclomatic number.

After losing his first amateur bout he attains some success and, despite his anxieties about marriage, seems poised to ascend the circuit ranks.

In graph-theoretic mathematics, the circuit rank, cyclomatic number, or nullity of an undirected graph is the minimum number of edges to remove from to remove all its cycles, making it into a forest.

The circuit rank controls the number of ears in an ear decomposition of a graph: in a biconnected graph with circuit rank , every open ear decomposition has exactly ears.

In graph theory, the circuit rank (or cyclomatic number) of a graph is the corank of the associated graphic matroid; it measures the minimum number of edges that must be removed from the graph to make the remaining edges form a forest.

With more than a dozen performing arts venues, the city's theater venue circuit ranks as the second largest in the United States after Manhattan's Broadway, the stages and old time film palaces are generally located along Woodward Avenue, the city's central thoroughfare, in the Downtown, Midtown, and New Center areas.

In a biconnected graph of circuit rank less than three (such as a cycle graph or theta graph) every cycle is peripheral, but every biconnected graph with circuit rank three or more has a non-peripheral cycle, which may be found in linear time.