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

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

Geometric Topology 2018-04-23 v2 Combinatorics

Authors: Yusuke Gokan , Hayato Katsumata , Katsuya Nakajima , Ayaka Shimizu , Yoshiro Yaguchi

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 $n \ge 7$ .

Keywords

graph theory graph pebbling spanning trees

Cite

@article{arxiv.1801.05197,
  title  = {A note on the cross-index of a complete graph based on a linear tree},
  author = {Yusuke Gokan and Hayato Katsumata and Katsuya Nakajima and Ayaka Shimizu and Yoshiro Yaguchi},
  journal= {arXiv preprint arXiv:1801.05197},
  year   = {2018}
}

Comments

28 pages, 18 figures

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