6 problems

Let $L$ be a finite set of graphs. A graph excludes $L$ as a minor if it contains no member of $L$ as a minor, where minors are obtained by edge contractions, edge deletions, and v…

A planar graph metric is a shortest-path metric on a finite planar graph whose edges have arbitrary weights. The Planar Conjecture. Every metric supported on a finite planar graph…

A planar metric is the shortest-path metric of a planar graph. An embedding of a metric space into $L_1$ has constant distortion if its distortion is bounded by a universal constan…

$k$-sum embedding conjecture. For any family of graphs $\mathcal F$, we have

GNRS conjecture. For every family of finite graphs $\mathcal F$, one has $c_1(\mathcal F)=O(1)$ if and only if $\mathcal F$ forbids some minor.

Planar embedding conjecture. Any planar metric admits an embedding into $L_1$ with constant distortion.