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How to find minimum cardinality maximal matching? I tried that pick a edge from highest degree vertex remove other edges from same vertex and so on.

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A 2-approximation can be obtained by returning a maximal matching, Call it M. Let OPT be a minimum maximal matching then for each edge in M OPT covers at least one of its endpoints thus: |OPT|>=|M|/2 It would be better if you’ll be more explicit about what you did and what you’d like the algorithm to achieve (analysis of your idea, approximation factor, so on...)

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