Abstract: | rc(k) Denotes the smallest integer such that any c-edge-coloring of the rc(k) vertex complete graph has a monochromatic k-connected subgraph. For any c, k ≧ 2, we show 2c(k – 1) + 1 ≦ rc(k) < 10/3 c(k – 1) + 1, and further that 4(k – 1) + 1 ≧ r2(k) < (3 + √ (k – 1) + 1. Some exact values for various Ramsey connectivity numbers are also computed. |