Creating 3-dimensional graph structures with DNA

We propose solving computational problems with DNA molecules by physically constructing 3-dimensional graph structures. Building blocks consisting of intertwined strands of DNA are used to represent graph edges and vertices. Diierent blocks would be combined to form all possible 3-dimensional structures representing a graph. The solution to the Hamiltonian cycle problem provided requires a constant number of steps regardless of the number of vertices. If a solution to the graph problem exists, then a fully closed circular molecule would be formed and can be isolated. This paper introduces a method of using 3D structures in computing which might signiicantly improve the eeciency of computations with DNA.