Maximum Induced Matching on Regular Graphs and Trees
نویسنده
چکیده
We investigate the complexity of the Maximum Induced Matching problem on regular graphs and trees. The problem is shown to be NP-complete on regular graphs of degree 4s for any positive integer s. We also looks at very simple approximation algorithms: we show that the largest induced matching in a regular graph of degree d can be approximated with a performance ratio less than d. However a simple reduction from maximum independent set shows that there exists a constant c larger than one such that Maximum Induced Matching problem is NP-hard to approximate with a performance ratio less than c even on regular graphs of degree four. Finally we describe a simple algorithm providing a linear time optimal solution to the Maximum Induced Matching problem if the input graph is a tree.
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تاریخ انتشار 1999