# Two Generalized Lower Bounds for the Circumference

## DOI:

https://doi.org/10.51408/1963-0002## Keywords:

Degree sums, Circumference, Minimum degree## Abstract

In 2013, the second author obtained two lower bounds for the length of a longest cycle C in a graph G in terms of the length of a longest path (a longest cycle) in G¡C and the minimum degree of G (Zh.G. Nikoghosyan, "Advanced Lower Bounds for the Circumference", Graphs and Combinatorics 29, pp. 1531-1541, 2013). In this paper we present two analogous bounds based on the average of the ¯rst i smallest degrees in G ¡ C for appropriate i instead of the minimum degree

## References

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

Zh.G. Nikoghosyan, '' Advanced lower bounds for the circumference", Graphs and Combinatorics 29, pp. 1531-1541,2013.

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*Mathematical Problems of Computer Science*,

*49*, 18–25. https://doi.org/10.51408/1963-0002

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