Efficient DNA Algorithms for Chromatic Number of Graph Problems

Adleman´s successful solution of a seven-vertex instance of the NP-complete Hamiltonian directed path problem by a DNA algorithm initiated the field of biomolecular computing. The graph-theoretic parameter that has probably received the most attention over the years is the chromatic number. The coloring problem is an NP-Complete problem. We provide DNA algorithms based on the molecular biology techniques to compute the vertex chromatic number of a given graph. The algorithms determine not merely the existence of a solution but yield all solutions (if any). The algorithm is highly parallel and has satisfactory fidelity. This work represents further evidence for the ability of DNA computing to solve NP-Complete problems.