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Chvátal-Erdős condition for pancyclicity - MaRDI portal

Chvátal-Erdős condition for pancyclicity (Q6601490)

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scientific article; zbMATH DE number 7910126
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Chvátal-Erdős condition for pancyclicity
scientific article; zbMATH DE number 7910126

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    Chvátal-Erdős condition for pancyclicity (English)
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    10 September 2024
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    A celebrated meta-conjecture of \textit{J. A. Bondy} [Colloq. Math. Soc. Janos Bolyai 10, 181--188 (1975; Zbl 0324.05115)] states that every non-trivial condition implying Hamiltonicity also implies pancyclicity (up to possibly a few exceptional graphs). The authors show that every graph \(G\) with \(\kappa(G) > (1+o(1))\alpha(G)\) is pancyclic, where \(\alpha(G)\) is the independence number and \(\kappa(G)\) the connectivity of \(G\). This extends the famous Chvátal-Erdős condition for Hamiltonicity and proves asymptotically a 30-year-old conjecture of \textit{B. Jackson} and \textit{O. Ordaz} [Discrete Math. 84, No. 3, 241--254 (1990; Zbl 0726.05043)]. An open problem concludes the paper.
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    Hamiltonicity
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    pancyclicity
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    Chvatál-Erdős theorem
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