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A graph G is said to be (p" pJ be-embeddable if there exist two subgraphs HI and H2 of G with H, U H2 = G so that H, is embedded on S", and H2 is embedded on S" where S" and S" are orientable surfaces of genera p, and p2 respectively. Several infinite families of bi-embeddings of complete graphs are exhibited. Results from a computer search for additional bi-embeddings are also included. Finally, an unsolved problem is presented.doi:10.1016/0012-365x(90)90320-h fatcat:yoqsuurmf5g5hhd225yo4u5uc4