Induced Matchings in Graphs of Bounded Maximum Degree

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

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