Edge colorings of the complete graph K149 and the lower bounds of three Ramsey numbers Original Research Article

An algorithm for calculating the clique numbers of circulant graphs is developed and applied to some circulant graphs of order 149. Then a constructive method is designed to study edge colorings of the complete graph Kp. Three new lower bounds for Ramsey numbers are obtained by using this method. They are: R(3,3,11)⩾150, R(3,4,8)⩾150, R(3,26)⩾150.