# An Approximate Generalization of the Okamura-Seymour Theorem

Nikhil Kumar

## Affiliation:

Hasso-Plattner institute, Potsdam, Germany.

## Time:

Tuesday, 31 January 2023, 09:30 to 10:30

• A201

## Organisers:

We consider the problem of multicommodity flows in planar graphs. Okamura and Seymour showed that if all the demands are incident on one face, then the cut-condition is sufficient for routing demands. We consider the following generalization of this setting and prove an approximate max flow-min cut theorem: for every demand edge, there exists a face containing both its end points. We show that the cut-condition is sufficient for routing Ω(1) -fraction of all the demands. To prove this, we give a L1-embedding of the planar metric which approximately preserves distance between all pair of points on the same face.