English

Spanning $F$-cycles in random graphs

Combinatorics 2021-06-21 v1

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 C4C_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 KrK_r-cycles.

Keywords

Cite

@article{arxiv.2106.10023,
  title  = {Spanning $F$-cycles in random graphs},
  author = {Alberto Espuny Díaz and Yury Person},
  journal= {arXiv preprint arXiv:2106.10023},
  year   = {2021}
}
R2 v1 2026-06-24T03:21:13.313Z