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


  • Zhora G. Nikoghosyan Institute for Informatics and Automation Problems of NAS RA




Hamilton cycle, Dominating cycle, Longest cycle, Large cycle


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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How to Cite

Nikoghosyan, Z. G. (2023). A Note on Large Cycles in Graphs Around Conjectures of Bondy and Jung. Mathematical Problems of Computer Science, 59, 7–15. https://doi.org/10.51408/1963-0097