The most important NP-Complete (logic) problem family!

In this paper, we prove that both problems for calculating the Banzhaf power index and the Shapley-Shubik power index for weighted majority games are NP-complete.

The purpose of this note is to give upper bounds (assuming P different from NP) on how far the generalizations of Skolem sequences can be taken while still hoping to resolve the existence question. We prove that the existence questions for both multi Skolem sequences and generalized Skolem sequences are strongly NP-complete. These results are significant strengthenings and simplifications of th...

We prove that if A is a large random relational structure (with at least one relation of arity at least 2) then the homomorphism extension problem EXT(A) is almost surely NP-complete.

We show that for each fixed n 3 it is NP-complete to determine whether an arbitrary graph can be edge-partitioned into subgraphs isomorphic to the complete graph Kn. The NP-completeness of a number of other edge-partition problems follows immediately.