# A Common Generalization of Dirac's Two Theorems

## Keywords:

Hamilton cycle, Longest cycle, Longest path, Minimum degree## Abstract

A theorem is proved including Dirac's two well-known theorems (1952) as particular cases.

## References

J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Macmillan, London and Elsevier, New York, 1976.

G. A. Dirac, “Some theorems on abstract graphs", Proc. London, Math. Soc., vol. 2, pp. 69-81, 1952.

K. Ozeki and T. Yamashita, “Length of longest cycles in a graph whose relative length is at least two", Graphs and Combinatorics, vol. 28, pp. 859-868, 2012.

J. A. Bondy, Basic Graph Theory: Paths and circuits, Handbook of Combinatorics, Elsevier, Amsterdam, vol. 1 ,2, 1990.

## Downloads

## Published

## How to Cite

*Mathematical Problems of Computer Science*,

*46*, 44–49. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/146

## Issue

## Section

## License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.