A lower bound on the $k$-conversion number of graphs of maximum degree $k+1$

Abstract

‎‎We derive a new sharp lower bound on the $k$-conversion number of graphs of maximum degree $k+1$‎. ‎This generalizes a result of W.~Staton [Induced forests in cubic graphs‎, ‎Discrete Math.‎,49 (‎1984) ‎175--178‎]‎, ‎which established a lower bound on the $k$-conversion number of $(k+1)$-regular graphs‎.