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Spanning $F$-cycles in random graphs

Part of: Graph theory

Published online by Cambridge University Press:  09 June 2023

Alberto Espuny Díaz Open the ORCID record for Alberto Espuny Díaz [Opens in a new window]  and
Yury Person Open the ORCID record for Yury Person [Opens in a new window]
Alberto Espuny Díaz*
Affiliation:
Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany
Yury Person
Affiliation:
Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany
*
Corresponding author: Alberto Espuny Díaz; Email: alberto.espuny-diaz@tu-ilmenau.de
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Abstract

We extend a recent argument of Kahn, Narayanan and Park ((2021) Proceedings of the AMS 149 3201–3208) 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.

Keywords

Random graphsthresholdspanning subgraph

MSC classification

Primary: 05C80: Random graphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 32 , Issue 5 , September 2023 , pp. 833 - 850
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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