The Decycling Number of Regular Graphs

N. Punnim

Abstract

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)$ := min${|S| : S \subseteq V (G) $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.