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Most prior work on online matching problems has been with the flexibility of keeping some vertices unmatched. We study three related online matching problems with the constraint of matching every vertex, i.e., with no rejections. We adopt a model in which vertices arrive in a uniformly random order and the edge-weights are arbitrary positive numbers. For the capacitated online bipartite matching problem in which the vertices of one side of the graph are offline and those of the other sidedoi:10.1609/aaai.v36i5.20437 fatcat:m6jjjnqfuze35bxrfwcunrug54