Feedback numbers of Kautz undirected graphs

The feedback number f(d, n) of the Kautz undirected graph UK(d, n) is the minimum number of vertices whose removal results in an acyclic graph. This paper shows ⌈(dn+1 − dn−1 − 1d(d +1)+1)/(2d − 1) ⌉ ≤ 2 f(d, n) ≤ dn − ( ⌊ d2 4 ⌋ +1)dn−2, which implies that f(2,n) = 2n−1,as obtained by Královič andRuˇzička [Information Processing Letters 86 (4) (2003), 191–196]