Abstract.
We show that every 4-representative graph embedding in the double torus contains a noncontractible cycle that separates the surface into two pieces. As a special case, every triangulation of the double torus in which every noncontractible cycle has length at least 4 has a noncontractible cycle that separates the surface into two pieces.
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Received: May 22, 2001 Final version received: August 22, 2002
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ID="*" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070613
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ID="†" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070430
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Ellingham, M., Zha, X. Separating Cycles in Doubly Toroidal Embeddings. Graphs and Combinatorics 19, 161–175 (2003). https://doi.org/10.1007/s00373-002-0491-y
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DOI: https://doi.org/10.1007/s00373-002-0491-y