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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Bibliographische Detailangaben
Hauptverfasser: Gokan, Yusuke, Katsumata, Hayato, Nakajima, Katsuya, Shimizu, Ayaka, Yaguchi, Yoshiro
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
Mathematics - Geometric Topology
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Beschreibung
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 $n \ge 7$.
DOI:10.48550/arxiv.1801.05197