Computing Cut Numbers

M. Ziegler, C. Sohler, in: Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG’00), 2000, pp. 73–79.

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Abstract
What is the minimum number of hyperplanes that slice all edges of the d-dimensional hypercube? The answers have been known for d<=4.<br>This work settles the problem for d=5 and d=6. More precisely, a computer search implies that 4 hyperplanes do not suffice for this purpose (but 5 do).<br>We also develop computational approaches for attacking this extremal problem from combinatorial geometry in higher dimensions. They allow us to determine for example all maximal sliceable subsets of hypercube edges up to dimension 7.
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Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG'00)
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73-79
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Ziegler M, Sohler C. Computing Cut Numbers. In: Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG’00). ; 2000:73-79.
Ziegler, M., & Sohler, C. (2000). Computing Cut Numbers. In Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG’00) (pp. 73–79).
@inproceedings{Ziegler_Sohler_2000, title={Computing Cut Numbers}, booktitle={Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG’00)}, author={Ziegler, Martin and Sohler, Christian}, year={2000}, pages={73–79} }
Ziegler, Martin, and Christian Sohler. “Computing Cut Numbers.” In Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG’00), 73–79, 2000.
M. Ziegler and C. Sohler, “Computing Cut Numbers,” in Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG’00), 2000, pp. 73–79.
Ziegler, Martin, and Christian Sohler. “Computing Cut Numbers.” Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG’00), 2000, pp. 73–79.

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