# Tangled Paths: A Random Graph Model from Mallows Permutations

@article{Enright2021TangledPA, title={Tangled Paths: A Random Graph Model from Mallows Permutations}, author={Jessica A. Enright and Kitty Meeks and William Pettersson and John Sylvester}, journal={ArXiv}, year={2021}, volume={abs/2108.04786} }

We introduce the random graph P ( n, q ) which results from taking the union of two paths of length n > 1, where the vertices of one of the paths have been relabelled according to a Mallows permutation with real parameter 0 < q ( n ) 6 1. This random graph model, the tangled path, goes through an evolution: if q is close to 0 the graph bears resemblance to a path and as q tends to 1 it becomes an expander. In an eﬀort to understand the evolution of P ( n, q ) we determine the treewidth and…

## One Citation

### The treewidth and pathwidth of graph unions

- MathematicsArXiv
- 2022

Given two n -vertex graphs G 1 and G 2 of bounded treewidth, is there an n -vertex graph G of bounded treewidth having subgraphs isomorphic to G 1 and G 2 ? Our main result is a negative answer to…

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