Planar Graph Metrics Embed into L1 with Constant Distortion
Source: github.com/openai/math/tree/main/preprints/Planar-Graph-Met…
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.
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API
curl /api/v1/records/openai-math/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion
curl -X POST /api/v1/records/openai-math/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'
OpenAI Math Dump Hits My Home | Rambling on Graphsminorfree.github.ioHung Le
Recent OpenAI Math dump have solutions to many long standing probems in Math and TCS. In the dump, two problems that I and my friends, notably Arnold Filtser, have studied for more than a decade, and published a few papers about this: