The Ramsey numbers for a cycle of length six or seven versus a clique of order seven Original Research Article

For two given graphs image and image, the Ramsey number image is the smallest integer image such that for any graph image of order image, either image contains image or the complement of image contains image. Let image denote a cycle of length m and image a complete graph of order image. It was conjectured that image for image and image. We show that image and image, and the latter result confirms the conjecture in the case when image.