We present a linear-time algorithm that, given a planar graph with m edges and maximum degree 3, finds an induced matching of size at least m/9. This is best possible.

, ,
, ,
S.I.A.M.
SIAM Journal on Discrete Mathematics
Networks and Optimization

Kang, R., Mnich, M., & Müller, T. (2012). Induced matchings in subcubic planar graphs. SIAM Journal on Discrete Mathematics, 26(3), 1383–1411.