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arXiv · 0910.1409

Pathwidth, trees, and random embeddings

James R. Lee·Anastasios Sidiropoulos
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Abstract

We prove that, for every $k=1,2,...,$ every shortest-path metric on a graph of pathwidth $k$ embeds into a distribution over random trees with distortion at most $c$ for some $c=c(k)$. A well-known conjecture of Gupta, Newman, Rabinovich, and Sinclair states that for every minor-closed family of graphs $F$, there is a constant $c(F)$ such that the multi-commodity max-flow/min-cut gap for every flow instance on a graph from $F$ is at most $c(F)$. The preceding embedding theorem is used to prove this conjecture whenever the family $F$ does not contain all trees.

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James R. Lee, Anastasios Sidiropoulos. 2012-10-06. Pathwidth, trees, and random embeddings. https://arxiv.org/abs/0910.1409

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