Ramsey numbers in octahedron graphs Original Research Article

The octahedron Ramsey number rO=rO(G1,…,Gt) is introduced as the smallest n such that any t-coloring of the edges of the octahedron graph On=K2n−nK2 contains for some i a subgraph Gi of color i. With r=r(G1,…,Gt) denoting the classical Ramsey number, rO is between r/2 and r. If all Giʹs are complete, then rO=r. If all Giʹs are certain stars, then rO=⌈r/2⌉. For all Gi with at most four vertices, all values rO(G1,G2) are listed.