Arc index of spatial graphs

Minjung Lee; Sungjong No; Seungsang Oh

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arXiv · 1711.08116

Arc index of spatial graphs

Minjung Lee·Sungjong No·Seungsang Oh

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Abstract

Bae and Park found an upper bound on the arc index of prime links in terms of the minimal crossing number. In this paper, we extend the definition of the arc presentation to spatial graphs and find an upper bound on the arc index $\alpha (G)$ of any spatial graph $G$ as $$\alpha(G) \leq c(G)+e+b,$$ where $c(G)$ is the minimal crossing number of $G$, $e$ is the number of edges, and $b$ is the number of bouquet cut-components. This upper bound is lowest possible.

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BibTeX RIS

Minjung Lee, Sungjong No, Seungsang Oh. 2017-11-22. Arc index of spatial graphs. https://arxiv.org/abs/1711.08116

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