Planar 3DM is NP-Complete

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.