Decycling bubble sort graphs

The decycling number of a graph GG is the minimum number of vertices whose removal from GG results in an acyclic subgraph. In this paper we show that the decycling number f(n)f(n) of the bubble sort graph BnBn satisfies these inequalities: n!(n−3)2(n−2)+1≤f(n)≤n!(2n−3)4(n−1).