Nonorientable triangular embeddings of complete graphs with arbitrarily large looseness |
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| Authors: | Vladimir P. Korzhik Jin Ho Kwak |
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| Affiliation: | a National University of Chernivtsi, Bogomoltsa St. 3/5, Chernivtsi 58012, Ukraine
b Department of Mathematics, Pohang University of Science and Technology, San 31 Hyoja Dong, Pohang 790-784, Korea |
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| Abstract: | The looseness of a triangular embedding of a complete graph in a closed surface is the minimum integer m such that for every assignment of m colors to the vertices of the embedding (such that all m colors are used) there is a face incident with vertices of three distinct colors. In this paper we show that for every p?3 there is a nonorientable triangular embedding of a complete graph with looseness at least p. |
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| Keywords: | Topological embedding Triangular embedding Complete graph Looseness Steiner triple system |
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