A best possible result for the square of a 2-block to be hamiltonian

A best possible result for the square of a 2-block to be hamiltonian

It is shown that for any choice of four different vertices x1,…,x4 in a 2-block G of order p>3, there is a hamiltonian cycle in G2 containing four different edges xiyi of E(G) for certain vertices yi, i=1,2,3,4. This result is best possible.

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Veröffentlicht in:Discrete mathematics 2021-01, Vol.344 (1), p.112158, Article 112158
Hauptverfasser: Ekstein, Jan, Fleischner, Herbert
Format: Artikel
Sprache:eng
Schlagworte:
Hamiltonian cycles
Square of graphs
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Zusammenfassung:It is shown that for any choice of four different vertices x1,…,x4 in a 2-block G of order p>3, there is a hamiltonian cycle in G2 containing four different edges xiyi of E(G) for certain vertices yi, i=1,2,3,4. This result is best possible.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2020.112158