A graph G = (V, E) is antimagic if there is a one-to-one correspondence f : E → {1, 2, . . . , |E|} such that for any two vertices u, v,It is known that bipartite regular graphs are antimagic and nonbipartite regular graphs of odd degree at least three are antimagic. Whether all non-bipartite regular graphs of even degree are antimagic remained an open problem. In this paper, we solve this problem and prove that all even degree regular graphs are antimagic.

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We address the following rainbow Ramsey problem: For posets P, Q what is the smallest number n such that any coloring of the elements of the Boolean lattice Bn either admits a monochromatic copy of P or a rainbow copy of Q. We consider both weak and strong (non-induced and induced) versions of this problem.

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