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arXiv · 2209.03325

Pancyclicity of Hamiltonian graphs

Nemanja Draganić·David Munhá Correia·Benny Sudakov
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Abstract

An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is pancyclic if it contains cycles of all lengths from $3$ up to $n$. In 1972, Erdős conjectured that every Hamiltonian graph with independence number at most $k$ and at least $n = Ω(k^2)$ vertices is pancyclic. In this paper we prove this old conjecture in a strong form by showing that if such a graph has $n = (2+o(1))k^2$ vertices, it is already pancyclic, and this bound is asymptotically best possible.

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Nemanja Draganić, David Munhá Correia, Benny Sudakov. 2023-07-20. Pancyclicity of Hamiltonian graphs. https://arxiv.org/abs/2209.03325

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