Spanning triangulations in random graphs

TL;DR

This paper determines the threshold probability for the emergence of spanning triangulations in random graphs for any polygon size, extending previous results for triangles.

Contribution

It generalizes the threshold for spanning triangulations from triangles to any polygon with 3 to n sides in random graphs.

Findings

Identifies the threshold probability for spanning triangulations of k-gons in random graphs.

Extends Bollobás and Frieze's triangle result to polygons with 3 ≤ k ≤ n.

Provides bounds up to constant factors for these thresholds.

Abstract

In 1991 Bollob\'{a}s and Frieze found the threshold for the emergence of a spanning triangulation of a triangle in the binomial random graph, up to a logarithmic factor. In this paper, we find the threshold probability for the emergence of a spanning triangulation of a $k$-gon for any $3\leq k\leq n$, up to a constant factor.