 
Summary: Embeddings of topological graphs:
Lossy invariants, linearization, and 2sums
Amit Chakrabarti # Alexander Jaffe + James R. Lee #+ Justin Vincent +
Abstract
We study the properties of embeddings, multicom
modity flows, and sparse cuts in minorclosed families
of graphs which are also closed under 2sums; this in
cludes planar graphs, graphs of bounded treewidth, and
constructions based on recursive edge replacement. In
particular, we show the following.
. Every graph which excludes K 4 as a minor (in par
ticular, seriesparallel graphs) admits an embed
ding into L 1 with distortion at most 2, confirming
a conjecture of Gupta, Newman, Rabinovich, and
Sinclair, and improving over their upper bound of
14. This shows that in every multicommodity flow
instance on such a graph, one can route a maximum
concurrent flow whose value is at least half the cut
bound. Our upper bound is optimal, as it matches
a recent lower bound of Lee and Raghavendra.
