Star-critical Ramsey numbers Original Research Article

The graph Ramsey number image is the smallest integer image such that every 2-coloring of the edges of image contains either a red copy of image or a blue copy of image. We find the largest star that can be removed from image such that the underlying graph is still forced to have a red image or a blue image. Thus, we introduce the star-critical Ramsey number image as the smallest integer image such that every 2-coloring of the edges of image contains either a red copy of image or a blue copy of image. We find the star-critical Ramsey number for trees versus complete graphs, multiple copies of image and image, and paths versus a 4-cycle. In addition to finding the star-critical Ramsey numbers, the critical graphs are classified for image, image and image.