On the Nonembeddability and Crossing Numbers of Some Kleinical Polyhedral Maps on the Torus |
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Authors: | Adrian Riskin |
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Affiliation: | (1) Department of Mathematics, Mary Baldwin College, Staunton, Virginia 24401, USA |
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Abstract: | We define a family of graph bundles over cycles which embed naturally on the Klein bottle and which are analogous to the celebrated toroidal grid graphs (cartesian product of a cycle with a cycle). We give a criterion for a polyhedral map on the Klein bottle to fail to embed on the torus, and use this to calculate toroidal crossing numbers of two one-parameter infinite families of our Kleinical graphs.Mathematics Subject Classification (1991): 05C10 |
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Keywords: | Crossing numbers Reimbedding Nontoroidal graphs |
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