An Algebraic Characterization of Rainbow Connectivity
  The use of algebraic techniques to solve combinatorial problems is studied in this paper. We formulate the rainbow connectivity problem as a system of polynomial equations. We first consider the case of two colors for which the problem is known to be hard and we then extend the approach to the general case. We also give a formulation of the rainbow connectivity problem as an ideal membership problem. 
Prabhanjan Ananth and Ambedkar Dukkipati
cs.DM