Inferring Evolutionary History from DNA Sequences

We are iiit,erested here in t w o related problems. The first is determining whether we can triangulate a vertex-colored graph without introducing edges between vertices of the same color. This is related to a fundamental problem for geneticists, that of using charact,er state information to construct evolutionary trees. lye demonstrate the polynomial equivalence of these problems. .4n important subproblem arises when the characters are based upon DNA sequences. Such characters assume up to 4 states. We present an O(n2k) algorithm for this case where n is the number of species and k is the number of characters.