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

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

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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Veröffentlicht in:arXiv.org 2018-04
Hauptverfasser: Gokan, Yusuke, Katsumata, Hayato, Nakajima, Katsuya, Shimizu, Ayaka, Yaguchi, Yoshiro
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Graph theory
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Zusammenfassung: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 \(n \ge 7\).
ISSN:2331-8422