Feedback vertex set

<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> discipline of <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, a feedback vertex set (FVS) of a <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graph</a> is a set of vertices whose removal leaves a graph without <a href="/facts/Cycle_(graph_theory)/Is44edrv">cycles</a> ("removal" means deleting the vertex and all edges adjacent to it). Equivalently, each FVS contains at least one vertex of any cycle in the graph. The feedback vertex set number of a graph is the size of a smallest FVS. Whether there exists a feedback vertex set of size at most k is an <a href="/facts/NP-complete/NFPv56DU">NP-complete</a> problem; it was among the <a href="/facts/Karp%2527s_21_NP-complete_problems/dqu5bBh0">first problems shown to be NP-complete</a>. It has wide applications in <a href="/facts/Operating_system/8XTuvMh2">operating systems</a>, <a href="/facts/Database_system/VYcpkevb">database systems</a>, and <a href="/facts/VLSI/l1Wgqr27">VLSI</a> chip design.
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Feedback vertex set open-in-new

Feedback vertex set