Ramsey numbers in octahedron graphs

Abstract The octahedron Ramsey number r O = r O ( G 1 ,…, G t ) is introduced as the smallest n such that any t-coloring of the edges of the octahedron graph O n = K 2 n − nK 2 contains for some i a subgraph G i of color i. With r = r ( G 1 ,…, G t ) denoting the classical Ramsey number, r O is between r /2 and r. If all G i 's are complete, then r O = r . If all G i 's are certain stars, then r O =⌈ r /2⌉. For all G i with at most four vertices, all values r O ( G 1 , G 2 ) are listed.