Copositive programming motivated bounds on the stability and the chromatic numbers (Q847835)

The authors introduce a copositive strengthening of the Lovász theta number toward the chromatic number. They show that the optimal value of this copositive strengthening is equal to the fractional chromatic number. Based on the proposed representation the authors investigate approximations of the chromatic number in the case of a vertex transitive graph. They provide some computational results indicating that the Lovász theta number can be strengthened significantly toward the fractional chromatic number on some Hamming graphs.