Abstract
LetG be a bipartite graph with natural edge weights, and letW be a function from the set of vertices ofG into natural numbers. AW-matching ofG is a subset of the set of edges ofG such that for each vertexv the total weight of edges in the subset incident tov does not exceedW(v). Letm be a natural number. We show that the problem of deciding whether there is aW-matching inG whose total weight is not less thanm is NP-complete even ifG is bipartite and its edge weights as well as theW(v)-constraints are constantly bounded.
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Lingas, A. An unfeasible matching problem. BIT 31, 591–597 (1991). https://doi.org/10.1007/BF01933174
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DOI: https://doi.org/10.1007/BF01933174