Abstract
A restriction of the three-dimensional matching problem 3DM, in which the associated bipartite graph is planar, is shown to remain NP-complete. The restriction is inspired by that of Lichtenstein's planar 3SAT (Planar formulae and their uses, SIAM J. Comput. 11 (1982), 329–343). Like Planar 3SAT, Planar 3DM is principally a tool for use in NP-completeness proofs for planar restrictions of other problems. Several examples of its applications in this respect are given.
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