Abstract
An induced matching is a matching in which each two edges of the matching are not connected by a joint edge. Induced matchings are well-studied combinatorial objects and a lot of consideration has been given to finding maximum induced matchings, which is an NP-complete problem. Specifically, finding maximum induced matchings in regular graphs is well-known to be NP-complete. A couple of papers lately showed a couple of simple greedy algorithm that approximate a maximum induced matching with a factor of \(d - {\frac{1}{2}}\) and d − 1 (different papers – different factors), where d is the degree of regularity. We show here a simple algorithm with an 0.75d + 0.15 approximation factor. The algorithm is simple – the analysis is not.
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Gotthilf, Z., Lewenstein, M. (2006). Tighter Approximations for Maximum Induced Matchings in Regular Graphs. In: Erlebach, T., Persinao, G. (eds) Approximation and Online Algorithms. WAOA 2005. Lecture Notes in Computer Science, vol 3879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11671411_21
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DOI: https://doi.org/10.1007/11671411_21
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