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arXiv · 2106.10023

Spanning $F$-cycles in random graphs

Alberto Espuny Díaz·Yury Person
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Abstract

We extend a recent argument of Kahn, Narayanan and Park (Proceedings of the AMS, to appear) about the threshold for the appearance of the square of a Hamilton cycle to other spanning structures. In particular, for any spanning graph, we give a sufficient condition under which we may determine its threshold. As an application, we find the threshold for a set of cyclically ordered copies of $C_4$ that span the entire vertex set, so that any two consecutive copies overlap in exactly one edge and all overlapping edges are disjoint. This answers a question of Frieze. We also determine the threshold for edge-overlapping spanning $K_r$-cycles.

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BibTeXRIS

Alberto Espuny Díaz, Yury Person. 2021-06-18. Spanning $F$-cycles in random graphs. https://arxiv.org/abs/2106.10023

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