Constructing a minimum genus embedding of the complete tripartite graph Kn,n,1 for odd n☆
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Add time:08/17/2019 Source:sciencedirect.com
We introduce a handle-inserting operation in order to construct a minimum genus embedding of the tripartite graph Kn,n,1 for odd n. The construction is used to solve the conjecture of Kurauskas that for odd n, Kn,n has an embedding of genus ⌈(n−1)(n−2)∕4⌉, such that one face is bounded by a Hamilton cycle. Such embeddings have an application to modeling road junctions with minimal number of bridges.
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