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The decycling number of regular graphs. (English) Zbl 1156.05317
Summary: For a graph \(G\) and \(S \subseteq V (G)\), if \(G - S\) is acyclic, then \(S\) is called a decycling set or feedback set of \(G\). The decycling number of \(G\) is defined to be \[ \phi(G) \, : = {\text{min}} \{|S| \, : \, S \subseteq V(G) \, {\text{is a decycling set}}\}. \] This paper reviews some recent results on interpolation and extremal problems on the decycling number of graphs, with an emphasis on the decycling number of regular graphs.

MSC:
05C35 Extremal problems in graph theory
05C38 Paths and cycles
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