Matching in Dynamic Graphs

Let G D .V;E/ be an undirected graph on n D jV j vertices and m D jEj edges. A matching in G is a set of edges M E such that no two edges in M share any vertex. Matching has been one of the most well-studied problems in algorithmic graph theory for decades [4]. A matching M is called maximum matching if the number of edges in M is maximum. The fastest known algorithm for maximum matching, due to Micali and Vazirani [5], runs in O.m p n/. A matching is said to be maximal if it is not strictly contained in any other matching. It is well known that a maximal matching achieves a factor 2 approximation of the maximum matching.