Abstract
It is proved that the questions whether a finite diagraph G has a kernel K or a Sprague—Grundy function g are NP-complete even if G is a cyclic planar digraph with degree constraints d out ( u)≤2, d in ( u)≤2 and d( u)≤3. These results are best possible (if P ≠ NP) in the sense that if any of the constraints is tightened, there are polynomial algorithms which either compute K and g or show that they do not exist. The proof uses a single reduction from planar 3-satisfiability for both problems.
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