Induced Matchings in Graphs of Bounded Maximum Degree

Abstract

For a graph $G$, let $\nu_s(G)$ be the size of a largest induced matching of $G$. We prove that $\nu_s(G)\geq\frac{n(G)}{(\lceil{\Delta}/{2}\rceil+1)(\lfloor{\Delta}/{2}\rfloor+1)}$ for every graph of sufficiently large maximum degree $\Delta$ and without isolated vertices. This bound is sharp. Moreover, there is a polynomial-time algorithm which computes induced matchings of the size stated above.