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Sharp thresholds for spanning regular subgraphs

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arxiv 2502.14794 v3 pith:XMCYDJQK submitted 2025-02-20 math.CO

classification math.CO
keywords regularfamilygraphssharpspanningthresholdalmostappearance
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abstract

We prove that $(1+o(1))\sqrt{e/n}$ is the sharp threshold for the appearance of the square of a Hamilton cycle in $G(n,p)$, confirming the conjecture of Kahn, Narayanan, and Park. We also find the exact asymptotics of the threshold for the emergence of a spanning subgraph isomorphic to a fixed graph $F$ for a wide family of $d$-regular graphs $F$. This family includes almost all $d$-regular graphs.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Universality in random graphs via optimal linking systems: trees and beyond

    math.CO 2026-08 conditional novelty 8.0 of 10

    An absolute constant C suffices for bounded-degree tree universality in G(n, C ln n/n), and cycle-factor universality is optimal up to constants via depth-optimal linking systems.

  2. On the threshold for triangulations inside convex polygons

    math.PR 2025-09 conditional novelty 6.0 of 10

    A random set of diagonals of a convex n-gon, each present with probability p, contains a triangulation with high probability whenever p > p* approximately 0.4916.

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