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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

On the Cartesian products with crossing number three

Zhangdong Ouyang1, Jing Wang2, Yuanqiu Huang3
1Department of Mathematics, Hunan First Normal University, Changsha 410205, P. R. China
2Department of Mathematics and Information Sciences, Changsha University, Changsha 410003, P. R. China
3Department of Mathematics, Hunan Normal University, Changsha 410081, P. R. China

Abstract

M. Klešc et al. characterized graphs \( G_1 \) and \( G_2 \) for which the crossing number of their Cartesian product \( G_1 \square G_2 \) equals one or two. In this paper, their results are extended by giving the necessary and sufficient conditions for all pairs of graphs \( G_1 \) and \( G_2 \) for which the crossing number of their Cartesian product \( G_1 \square G_2 \) equals three, if one of the graphs \( G_1 \) and \( G_2 \) is a cycle.

Keywords: Graph; Drawing; Crossing number; Cartesian product.
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Citation
Zhangdong Ouyang, Jing Wang, Yuanqiu Huang. On the Cartesian products with crossing number three[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 115. 245-251. .