The nonorientable genus of complete tripartite graphs

Authors:
M. N. Ellingham;Chris Stephens;Xiaoya Zha
Affiliations:
Department of Mathematics, Vanderbilt University, Nashville, TN;Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN;Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

Citing 6
Cited 1

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Topological graph theory
Surgical techniques for construction minimal orientable imbeddings and joins and compositions of graphs

Surgical techniques for construction minimal orientable imbeddings and joins and compositions of graphs
The medial graph and voltage-current duality

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On the genus of joins and compositions of graphs

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Orientable and Nonorientable Genera for Some Complete Tripartite Graphs

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Counterexamples to the nonorientable genus conjecture for complete tripartite graphs

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The nonorientable genus of joins of complete graphs with large edgeless graphs

Journal of Combinatorial Theory Series B

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Abstract

In 1976, Stahl and White conjectured that the nonorientable genus of Kl,m.n, where l ≥ m ≥ n, is ⌈(l-2)(m + n - 2)/2⌉. The authors recently showed that the graphs K3,3,3, K4,4,1, and K4,4,1 are counterexamples to this conjecture. Here we prove that apart from these three exceptions, the conjecture is true. In the course of the paper we introduce a construction called a transition graph, which is closely related to voltage graphs.