A. Frieze

activity

20242026

collaborators

8 papers

math.CO2026

Coloring powers of random graphs

Alan Frieze, Ross Kang, Aditya Raut +2

Given a graph $G$ and an integer $r \geq 1$ , the $r$ th power $G^{r}$ of $G$ is the graph obtained from $G$ by adding edges for all pairs of distinct vertices at distance at most $r$ fr…

math.CO2026

Edge disjoint Hamilton cycles in random digraphs of constant minimum degree

Colin Cooper, Alan Frieze

We study the existence of directed Hamilton cycles in random digraphs with $m$ edges where we condition on minimum in- and out-degree $\d \ge k+1$, where $k \geq 1$ . Denote such a r…

math.CO2025

On Minimum Cost Rainbow Structures

Patrick Bennett, Quentin Dubroff, Alan Frieze +1

We discuss the expected minimum cost of rainbow spanning trees and Hamilton cycles in randomly edge colored random graphs.

math.CO2025

Some Maker-Breaker games on hypergraphs

Patrick Bennett, Alan Frieze, Wesley Pegden

We consider some biased Maker-Breaker games. Starting with the complete $k$ -uniform hypergraph on $n$ vertices, at each turn Maker claims one edge, and then Breaker claims $b$ edge…

math.CO2025

Loose paths in random ordered hypergraphs

Andrzej Dudek, Alan Frieze, Wesley Pegden

We consider the length of {\em ordered loose paths} in the random $r$ -uniform hypergraph $H = H^{(r)} (n, p)$ . A ordered loose path is a sequence of edges $E_{1}, E_{2}, \dots, E_{ℓ}$ wher…

math.PR2025

Aspects of a randomly growing cluster in $\reals^d,d\geq 2

Alan Frieze, Ravi Kannan, Wesley Pegden

We consider a simple model of a growing cluster of points in $ℜ^{d}, d \geq 2$ . Beginning with a point $X_{1}$ located at the origin, we generate a random sequence of points $X_1,X_2,\…