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In this paper, we have developed a fully-dynamic algorithm for maintaining cardinality of maximum-matching in a tree using the construction of top-trees. The time complexities are as follows: 1. Initialization Time: O(n(log(n))) to build the Top-tree. 2. Update Time: O(log(n)) 3. Query Time: O(1) to query the cardinality of maximum-matching and O(log(n)) to find if a particular edge is matched.arXiv:0901.2900v1 fatcat:ze6ze7rgvfdlxfuurd2vu4f6ye