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arXiv · 1103.4227

The crossing number of locally twisted cubes

Haoli Wang·Xirong Xu·Yuansheng Yang·Bao Liu·Wenping Zheng·Guoqing Wang
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Abstract

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory {\bf 59}, 145--161 (2008)] which solves the upper bound conjecture on the crossing number of $n$-dimensional hypercube proposed by Erdős and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.

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Haoli Wang, Xirong Xu, Yuansheng Yang, Bao Liu, Wenping Zheng, Guoqing Wang. 2011-03-22. The crossing number of locally twisted cubes. https://arxiv.org/abs/1103.4227

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