Random walks on edge colored random graphs

TL;DR

This paper studies random walks on edge-colored random graphs where edge colors indicate costs, analyzing how the walk's behavior is affected by the cost structure, particularly focusing on red and blue edges with different traversal costs.

Contribution

It introduces a model of random walks on edge-colored graphs with cost implications, providing new insights into how edge costs influence walk dynamics.

Findings

Red edges increase traversal cost and affect walk patterns.

Blue edges allow free movement, influencing walk efficiency.

Cost structure impacts the mixing time and cover time of the walk.

Abstract

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. Blue edges are free to use, whereas red edges incur a unit cost every time they are traversed.