### Abstract

In this talk we will construct a class of SAT-formulae based on Eulerian graphs. The satisfiablility of these formulae depend on the number of edges in the Eulerian graph and it is easy to construct extremely similar formulae which differ in satisfiabillity. The structure of the graph can also be used to tune the formulae to be resitant to several modern enhancements of the basic DPLL-algorithm. Some possible connections to the hardness of random K-SAT formulae will also be mentioned.