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Hamiltonian Cycles in Squares of Vertex-Unicyclic Graphs

Published online by Cambridge University Press:  20 November 2018

Herbert Fleischner  and
Arthur M. Hobbs
Herbert Fleischner
Affiliation:
Institut für Informationsverarbeitung Wien, Austria
Arthur M. Hobbs
Affiliation:
Institut für Informationsverarbeitung Wien, Austria
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Extract

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In this paper we determine necessary and sufficient conditions for the square of a vertex-unicyclic graph to be Hamiltonian. The conditions are simple and easily checked. Further, we show that the square of a vertex-unicyclic graph is Hamiltonian if and only if it is vertex-pancyclic.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 2 , 01 June 1976 , pp. 169 - 172
Copyright
Copyright © Canadian Mathematical Society 1976

Footnotes

(1)

Partial support for this work was received from the National Science Foundation Grant No. GP-43696.

References

1. Behzad, M. and Chartrand, G., Introduction to the Theory of Graphs, Allyn and Bacon, Inc. (1972).Google Scholar
2. Fleischner, H., Über Hamiltonsche Linien im Quadrat kubischer und pseudokubischer Graphen, Mathematische Nachrichten 49 (1971), 163–171.Google Scholar
3. Hobbs, A. M., Hamiltonian Squares of Cacti, J. Comb. Theory (to appear).Google Scholar
4. Tutte, W. T., Connectivity in Graphs, U. of Toronto Press, (1966).CrossRefGoogle Scholar