• Corpus ID: 236965540

Tangled Paths: A Random Graph Model from Mallows Permutations

  title={Tangled Paths: A Random Graph Model from Mallows Permutations},
  author={Jessica A. Enright and Kitty Meeks and William Pettersson and John Sylvester},
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… 

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