Jakob Hofstad

activity

20192026

most citedTwo-Point Concentration of the Independence Number of the Random Graph

2 citations · 2 across the 5 of their papers we have counts for

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math.CO2026

Concentration of the largest induced tree size of $G_{n, p}$ around the standard expectation threshold

Jakob Hofstad

Let $T (G)$ be the size of the largest induced tree of $G$ , and let $G_{n, p}$ be the binomial random graph. Kamaldinov, Skorkin, and Zhukovskii proved that $T (G_{n, p})$ equals one o…

math.CO2024

A note on Two-Point Concentration of the Independence Number of $G_{n, m}$

Tom Bohman, Jakob Hofstad

We show that the independence number of $G_{n, m}$ is concentrated on two values for $n^{5/4 + ε} < m \leq (2 n)$ . This result establishes a distinction between $G_{n, m}$ and…

math.CO2023

Behavior of the Minimum Degree Throughout the $d$ -process

Jakob Hofstad

The $d$ -process generates a graph at random by starting with an empty graph with $n$ vertices, then adding edges one at a time uniformly at random among all pairs of vertices which…

math.CO2022★ 2 cited

Two-Point Concentration of the Independence Number of the Random Graph

Tom Bohman, Jakob Hofstad

We show that the independence number of $G_{n, p}$ is concentrated on two values if $n^{- 2/3 + ε} < p \leq 1$ . This result is roughly best possible as an argument of Sah and Sawhney…

math.CO2022

A Critical Probability for Biclique Partition of $G_{n, p}$

Tom Bohman, Jakob Hofstad

The biclique partition number of a graph $G = (V, E)$ , denoted $b p (G)$ , is the minimum number of pairwise edge disjoint complete bipartite subgraphs of $G$ so that each edge of $G$ b…

Concentration of the largest induced tree size of Gn,p​ around the standard expectation threshold

A note on Two-Point Concentration of the Independence Number of Gn,m​

Behavior of the Minimum Degree Throughout the d-process

Two-Point Concentration of the Independence Number of the Random Graph

A Critical Probability for Biclique Partition of Gn,p​

Concentration of the largest induced tree size of $G_{n, p}$ around the standard expectation threshold

A note on Two-Point Concentration of the Independence Number of $G_{n, m}$

Behavior of the Minimum Degree Throughout the $d$ -process

A Critical Probability for Biclique Partition of $G_{n, p}$