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.

induced matchings, subcubic planar graphs, strong chromatic index
Factorization, matching, partitioning, covering and packing (msc 05C70), Graph algorithms (msc 05C85), Graph theory (including graph drawing) (msc 68R10)
Logistics (theme 3)
SIAM Journal on Discrete Mathematics
Networks and Optimization

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