OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
Resolves the planar and bounded-treewidth cases of the Gupta–Newman–Rabinovich–Sinclair conjecture. Shortest-path metrics of finite connected graphs with arbitrary positive edge lengths embed into real L_(1) with universal distortion for planar graphs, and distortion depending only on treewidth for bounded-treewidth graphs. The corresponding multicommodity flow–cut gaps are uniformly bounded.
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We prove that every finite connected planar graph with arbitrary positive real edge lengths embeds into real L_(1) with a universal distortion bound. This resolves the planar embedding conjecture positively.
This PDF is listed in OpenAI's formalization catalogue. See the scope and dependencies before interpreting coverage.
For every fixed treewidth bound, the shortest-path metrics of finite connected graphs with arbitrary positive real edge lengths embed into real L_(1) with uniformly bounded distortion. This resolves the bounded-treewidth case of the Gupta–Newman–Rabinovich–Sinclair conjecture positively.
This PDF is listed in OpenAI's formalization catalogue. See the scope and dependencies before interpreting coverage.
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