Alan M. Frieze

collaborators

4 papers

math.CO2025

Random walks on edge colored random graphs

Colin Cooper, Alan Frieze

We consider random walks on edge coloured random graphs, where the colour of an edge reflects the cost of using it. In the simplest instance, the edges are coloured red or blue. Bl…

math.CO2025

Rainbow copies of spanning subgraphs

Colin Cooper, Alan Frieze

Let $G_{n, p}^{[I^º]}$ denote the space of $n$ -vertex edge coloured graphs, where each edge occurs independently with probability $p$ . The colour of each existing edge is chosen inde…

math.CO2025

Cover time of random subgraphs of the hypercube

Colin Cooper, Alan Frieze, Wesley Pegden

$Q_{n, p}$ , the random subgraph of the $n$ -vertex hypercube $Q_{n}$ , is obtained by independently retaining each edge of $Q_{n}$ with probability $p$ . We give precise values for the cov…

math.CO2025

The threshold for loose Hamilton cycles in random hypergraph

Alan Frieze, Xavier Perez-Gimenez

We show that w.h.p.\ the random $r$ -uniform hypergraph $H_{n, m}$ contains a loose Hamilton cycle, provided $r \geq 3$ and $m \geq \frac{( 1 + I ^ µ ) n l o g n}{r}$ , where $I^µ$ is an arbitrary…