Separating Cycles in Doubly Toroidal Embeddings |
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| Authors: | MN Ellingham Xiaoya Zha |
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| Institution: | (1) Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA. e-mail: mne@math.vanderbilt.edu, US;(2) Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA. e-mail: xzha@mtsu.edu, US |
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| 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.
Received: May 22, 2001 Final version received: August 22, 2002
RID="*"
ID="*" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070613
RID="†"
ID="†" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070430 |
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