Decycling cubes and grids (Q2725019)

The decycling number of a graph \(G\) is the smallest size of a decycling set, that is, a vertex set whose deletion removes all cycles from \(G\). The authors give some improvements on lower and upper bounds for the decycling numbers of \(n\)-cubes and grid graphs obtained by Beineke-Vandell in 1997; see \textit{L. W. Beineke} and \textit{R. C. Vandell} [J. Graph Theory 25, No. 1, 59-77 (1997; Zbl 0870.05033)]. The new bounds are determined by finding decycling sets of key subgraphs of these graphs.