Induced Matchings in Regular Graphs and Trees
This paper studies the complexity of the Maximum Induced Matching problem (MIM) in regular graphs and trees. We show that the largest induced matchings in a regular graph of degree d can be approximated with a performance ratio less than d. However MIM is NP-hard to approximate within some constant c > 1 even if the input is restricted to various classes of bounded degree and regular graphs. Finally we describe a simple algorithm providing a linear time optimal solution to MIM if the input graph is a tree.
KeywordsPolynomial Time Bipartite Graph Regular Graph Performance Ratio Input Graph
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- 2.P. Berman and M. Karpinski. On Some Tighter Inapproximability Results. In Proc. 26th I.C.A.L.P., Springer-Verlag, 1999. 96Google Scholar
- 4.P. Crescenzi. A Short Guide to Approximation Preserving Reductions. In Proc. 12th Conf. on Comput. Complexity, pages 262–273, Ulm, 1997. 93Google Scholar
- 8.M. R. Garey and D. S. Johnson. Computer and Intractability, a Guide to the Theory of NP-Completeness. Freeman and Company, 1979. 94Google Scholar
- 10.S. Khanna and S. Muthukrishnan. Personal communication. 94Google Scholar
- 12.C. Papadimitriou. Computational Complexity. Addison-Wesley, 1994. 93Google Scholar