Induced matchings in graphs of degree at most 4
  We show that if $G$ is a connected graph of maximum degree at most $4$, which is not $C_{2,5}$, then the strong matching number of $G$ is at least $\frac{1}{9}n(G)$. This bound is tight and the proof implies a polynomial time algorithm to find an induced matching of this size. 
Viet Hang Nguyen
cs.DM math.CO