Resumen de Threshold Ramsey multiplicity for odd cycles
David Conlon, Jacob Fox, Benny Sudakov, Fang Wei
The Ramsey number r(H) of a graph H is the minimum n such that any two-coloring of the edges of the complete graph Kn contains a monochromatic copy of H. The threshold Ramsey multiplicity m(H) is then the minimum number of monochromatic copies of H taken over all two-edgecolorings of Kr(H) . The study of this concept was first proposed by Harary and Prins almost fifty years ago. In a companion paper, the authors have shown that there is a positive constant c such that the threshold Ramsey multiplicity for a path or even cycle with k vertices is at least (ck) k, which is tight up to the value of c. Here, using different methods, we show that the same result also holds for odd cycles with k vertices.
