# Non-hamiltonian 4/5-tough maximal planar graphs

@article{Harant1995Nonhamiltonian4M,
title={Non-hamiltonian 4/5-tough maximal planar graphs},
author={Jochen Harant and Peter J. Owens},
journal={Discret. Math.},
year={1995},
volume={147},
pages={301-305}
}
• Published 16 December 1995
• Mathematics
• Discret. Math.

## Figures and Tables from this paper

More than one tough chordal planar graphs are Hamiltonian
• Mathematics
J. Graph Theory
• 1999
It is proved that for any " > 0 there is a 1-tough chordal planar graph G " such that the length of a longest cycles of G " is less than "jV (G)j".
An update on non-Hamiltonian $\frac{5}{4}$-tough maximal planar graphs
Studying the shortness of longest cycles in maximal planar graphs, we improve the upper bound on the shortness exponent of the class of $\frac{5}{4}$-tough maximal planar graphs presented by Harant
The Relation Between Hamiltonian and 1-Tough Properties of the Cartesian Product Graphs
• Mathematics
Graphs Comb.
• 2021
The relation between Hamiltonicity and toughness of a graph is a long standing research problem and it is shown that the following three statements are equivalent: (i) P_n\square H is Hamiltonian; (ii) H is-tough; and (iii) $H$ has a path factor.
Toughness in Graphs – A Survey
• Mathematics
Graphs Comb.
• 2006
This survey has attempted to bring together most of the results and papers that deal with toughness related to cycle structure into a few self explanatory categories.
Separating 3-cycles in plane triangulations
• Mathematics
Discret. Math.
• 2001
Toughness in Graph s-AS urvey
• Mathematics
• 2006
In this survey we have attempted to bring together most of the results and papers that deal with toughness related to cycle structure. We begin with a brief introduction and a section on terminology

## References

SHOWING 1-6 OF 6 REFERENCES
Shortness Exponents of Families of Graphs
• Mathematics
J. Comb. Theory, Ser. A
• 1973
Shortness expotients of families of graphs
• J. Combin. Theory
• 1973