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The Kuratowski covering conjecture for graphs of order less than 10
| Title: | The Kuratowski covering conjecture for graphs of order less than 10 |
| Author: | Hur, Suhkjin |
| Description: | Kuratowski proved that a finite graph embeds in the plane if it does not contain a subdivision of either K5 or K3,3, called Kuratowski subgraphs. A conjectured generalization of this result to all nonorientable surfaces says that a finite graph embeds in the nonorientable surface of genus g̃ if it does not contain g̃+1 Kuratowski subgraphs such that the union of each pair of these fails to embed in the projective plane, the union of each triple of these fails to embed in the Klein bottle if g̃ ≥ 2, and the union of each triple of these fails to embed in the torus if g̃ ≥ 3. We prove this conjecture for all graphs of order < 10. |
| Permanent Link: |
http://rave.ohiolink.edu/etdc/view?acc_num=osu1209141894
http://hdl.handle.net/2374.OX/5756 |
| Date: | 2008 |
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