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arXiv · 2309.14197

Resilience for Loose Hamilton Cycles

José D. Alvarado·Yoshiharu Kohayakawa·Richard Lang·Guilherme O. Mota·Henrique Stagni
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Abstract

We study the emergence of loose Hamilton cycles in subgraphs of random hypergraphs. Our main result states that the minimum $d$-degree threshold for loose Hamiltonicity relative to the random $k$-uniform hypergraph $H_k(n,p)$ coincides with its dense analogue whenever $p \geq n^{- (k-1)/2+o(1)}$. The value of $p$ is approximately tight for $d>(k+1)/2$. This is particularly interesting because the dense threshold itself is not known beyond the cases when $d \geq k-2$.

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José D. Alvarado, Yoshiharu Kohayakawa, Richard Lang, Guilherme O. Mota, Henrique Stagni. 2023-09-25. Resilience for Loose Hamilton Cycles. https://arxiv.org/abs/2309.14197

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