Two greedy consequences for maximum induced matchings

We prove that, for every integer d   with d≥3d≥3, there is an approximation algorithm for the maximum induced matching problem restricted to {C3,C5}{C3,C5}-free d  -regular graphs with performance ratio 0.7083¯d+0.425, which answers a question posed by Dabrowski et al. (Theoret. Comput. Sci. 478 (2013) 33–40). Furthermore, we show that every graph with m edges that is k-degenerate and of maximum degree at most d   with k