%0 Journal Article
%T Two Greedy Consequences for Maximum Induced Matchings
%A Dieter Rautenbach
%J Mathematics
%D 2015
%I arXiv
%X We prove that, for every integer $d$ with $d\geq 3$, there is an approximation algorithm for the maximum induced matching problem restricted to $\{ C_3,C_5\}$-free $d$-regular graphs with performance ratio $0.708\bar{3}d+0.425$, which answers a question posed by Dabrowski et al. (Theor. 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 $k<d$, has an induced matching with at least $m/((3k-1)d-k(k+1)+1)$ edges.
%U http://arxiv.org/abs/1507.04145v1