The orientable genus of some joins of complete graphs with large edgeless graphs |
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Authors: | MN Ellingham D Christopher Stephens |
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Institution: | a Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA b Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA |
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Abstract: | In an earlier paper the authors showed that with one exception the nonorientable genus of the graph with m≥n−1, the join of a complete graph with a large edgeless graph, is the same as the nonorientable genus of the spanning subgraph . The orientable genus problem for with m≥n−1 seems to be more difficult, but in this paper we find the orientable genus of some of these graphs. In particular, we determine the genus of when n is even and m≥n, the genus of when n=2p+2 for p≥3 and m≥n−1, and the genus of when n=2p+1 for p≥3 and m≥n+1. In all of these cases the genus is the same as the genus of Km,n, namely ⌈(m−2)(n−2)/4⌉. |
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Keywords: | Orientable genus Join Hamilton cycle embedding |
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