Two maps on one surface (Q2725321)
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scientific article; zbMATH DE number 1619121
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two maps on one surface |
scientific article; zbMATH DE number 1619121 |
Statements
16 April 2002
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embeddings
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surface
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edge crossings
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torus
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Two maps on one surface (English)
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The authors consider simultaneous embeddings of two graphs on a surface. The problem is to find equivalent embeddings of the two given embeddings such that the total number of edge crossings is minimum. (No two edges in the same graph cross.) For the projective plane the problem is solved completely: The minimum number of crossings is the product of the lengths of the shortest noncontractible cycles in the dual graphs. Upper and lower bounds in the torus case are also presented, and the general case is briefly discussed.
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