{"id":"openai-math/Paired-states-and-Hamiltonian-cycles-in-cubic-bipartite-planar-graphs","pdf":"https://github.com/openai/math/blob/main/preprints/Paired-states-and-Hamiltonian-cycles-in-cubic-bipartite-planar-graphs-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Paired-states-and-Hamiltonian-cycles-in-cubic-bipartite-planar-graphs-September-24-2026","tags":["graph-theory","hamiltonian-cycles","planar-graphs"],"score":0,"title":"Paired states and Hamiltonian cycles in cubic bipartite planar graphs","domain":"Combinatorics","family":"180","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We prove Barnette's conjecture: every finite simple cubic bipartite planar 3-vertex-connected graph has a Hamiltonian cycle.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.30490","date":"2026-10-21","kind":"web","site":"arXiv.org","text":"Barnette's conjecture states that every cubic 3-connected bipartite planar graph has a Hamiltonian cycle. We present a digested exposition of OpenAI's generated proof of Barnette's conjecture \\cite{openai-barnette}.","added":"2026-10-24","title":"A note on the proof of Barnette's conjecture","author":"Zhentao Li","record":"arxiv/2610.30490"}],"formalized":false,"family_title":"Barnette’s Hamiltonian-cycle conjecture"}