Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. Many NPhard problems can be solved in polynomial time if they are restricted on trapezoid graphs. A matching in a graph is a set of pairwise disjoint edges, and a maximum matching is a matching of maximum size. In this paper, we first propose an O(n(log n)3 ) algorithm for finding a maximum matching in trapezoid graphs, then improve the complexity to O(n(log n)2 ). Finally, we generalize this algorithm to a larger graph class, namely k-trapezoid graphs. To the best of our knowledge, these are the first efficient maximum matching algorithms for trapezoid graphs.

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