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arXiv · 1801.05197

A note on the cross-index of a complete graph based on a linear tree

Yusuke Gokan·Hayato Katsumata·Katsuya Nakajima·Ayaka Shimizu·Yoshiro Yaguchi
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Abstract

In this paper it is shown that a complete graph with $n$ vertices has an optimal diagram, i.e., a diagram whose crossing number equals the value of Guy's formula, with a free maximal linear tree and without free hamiltonian cycles for any odd integer $n \ge 7$.

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Yusuke Gokan, Hayato Katsumata, Katsuya Nakajima, Ayaka Shimizu, Yoshiro Yaguchi. 2018-04-20. A note on the cross-index of a complete graph based on a linear tree. https://arxiv.org/abs/1801.05197

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