任意有环有向图都可以被转化为有向无环图。只要从图中移除<font color="#ff8000"> '''反馈节点集 Feedback vertex set''' </font>或<font color="#ff8000"> '''反馈边集 Feedback arc set''' </font>,即对于图中每个环,至少包括环中一个顶点或边的集合。不过,找到反馈节点或边的最小集合是[[NP困难]]问题。<ref>{{citation | last1=Garey | first1=Michael R. | authorlink1=Michael Garey | last2=Johnson | first2=David S. | authorlink2=David S. Johnson | year=1979| title=[[Computers and Intractability|Computers and Intractability: A Guide to the Theory of NP-Completeness]]| publisher=[[W. H. Freeman and Company|W. H. Freeman]]| isbn=0-7167-1045-5| chapter = Problems GT7 and GT8| pages = 191–192}}</ref> 另外一种方法将有环有向图去环的方法是将每个强连通分量[[边收缩|收缩]]为一个顶点。<ref>{{citation|title=Structural Models: An Introduction to the Theory of Directed Graphs|last1=Harary|first1=Frank|author1-link=Frank Harary|last2=Norman|first2=Robert Z.|last3=Cartwright|first3=Dorwin|publisher=John Wiley & Sons|year=1965|page=63}}.</ref> 对于无环图,它的最小反馈顶点或边集为[[空集]],它的强连通分量则为自身。 | 任意有环有向图都可以被转化为有向无环图。只要从图中移除<font color="#ff8000"> '''反馈节点集 Feedback vertex set''' </font>或<font color="#ff8000"> '''反馈边集 Feedback arc set''' </font>,即对于图中每个环,至少包括环中一个顶点或边的集合。不过,找到反馈节点或边的最小集合是[[NP困难]]问题。<ref>{{citation | last1=Garey | first1=Michael R. | authorlink1=Michael Garey | last2=Johnson | first2=David S. | authorlink2=David S. Johnson | year=1979| title=[[Computers and Intractability|Computers and Intractability: A Guide to the Theory of NP-Completeness]]| publisher=[[W. H. Freeman and Company|W. H. Freeman]]| isbn=0-7167-1045-5| chapter = Problems GT7 and GT8| pages = 191–192}}</ref> 另外一种方法将有环有向图去环的方法是将每个强连通分量[[边收缩|收缩]]为一个顶点。<ref>{{citation|title=Structural Models: An Introduction to the Theory of Directed Graphs|last1=Harary|first1=Frank|author1-link=Frank Harary|last2=Norman|first2=Robert Z.|last3=Cartwright|first3=Dorwin|publisher=John Wiley & Sons|year=1965|page=63}}.</ref> 对于无环图,它的最小反馈顶点或边集为[[空集]],它的强连通分量则为自身。 |