# A Note on Large Cycles in Graphs Around Conjectures of Bondy and Jung

## DOI:

https://doi.org/10.51408/1963-0097## Keywords:

Hamilton cycle, Dominating cycle, Longest cycle, Large cycle## Abstract

New sufficient conditions are derived for generalized cycles (including Hamilton and dominating cycles as special cases) in an arbitrary k-connected (k = 1, 2, ...) graph, which prove the truth of Bondy’s (1980) famous conjecture for some variants significantly improving the result expected by the given hypothesis. Similarly, new lower bounds for the circumference (the length of a longest cycle) are established for the reverse hypothesis proposed by Jung (2001) combined inspiring new improved versions of the original conjectures of Bondy and Jung.

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*Mathematical Problems of Computer Science*,

*59*, 7–15. https://doi.org/10.51408/1963-0097

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