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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
##### Keywords:
decycling set; decycling number; regular graph