The orientable genus of certain complete tripartite graphs
نویسندگان
چکیده
In 1969, White conjectured that the orientable genus of the complete tripartite graph Kl,m,n, with l ≥ m ≥ n, is ⌈ (l−2)(m+n−2) 4 ⌉ . In this talk we describe progress on this conjecture. We can show that White’s conjecture is true in the cases where (m, n), reduced modulo 4, is (0, 0), (0, 2), (1, 1), (2, 0), (2, 1), (2, 2), (2, 3) or (3, 3). We discuss similarities and differences between our approach to this problem and our approach to the corresponding problem for the nonorientable genus of complete tripartite graphs, which we recently solved.
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