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FeedbackVertexSetNumber on LabeledGraph ​

The fewest vertices whose deletion leaves a graph with no cycle.

On LabeledGraph

FindStat's St001331: the vertices less the largest induced forest. The graph with no vertices gives 0.

Called as CombinatorialStat(x, "FeedbackVertexSetNumber"). The head's page has its examples.

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Distribution

Over LabeledGraphs at each size, tallied here in your browser; sizes past 6 are not offered.

FindStat St001331

The size of the minimal feedback vertex set.

ObjectValue
([],1)0
([],2)0
([],3)0
([],4)0
([],5)0
([],6)0
([],7)0
([(0,1)],2)0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001331 has the rest.