Pathwidth, trees, and random embeddings

نویسندگان

  • James R. Lee
  • Anastasios Sidiropoulos
چکیده

We prove that, for every integer k ≥ 1, every shortest-path metric on a graph of pathwidth k embeds into a distribution over random trees with distortion at most c = c(k), independent of the graph size. A well-known conjecture of Gupta, Newman, Rabinovich, and Sinclair [GNRS04] 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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عنوان ژورنال:
  • Combinatorica

دوره 33  شماره 

صفحات  -

تاریخ انتشار 2013