{"id":"openai-math/The-Factor-Two-Hardness-Threshold-for-Vertex-Cover","pdf":"https://github.com/openai/math/blob/main/preprints/The-Factor-Two-Hardness-Threshold-for-Vertex-Cover-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Factor-Two-Hardness-Threshold-for-Vertex-Cover-September-23-2026","tags":["computational-complexity","vertex-cover","approximation-algorithms","graph-theory"],"score":0,"title":"The Factor-Two Hardness Threshold for Vertex Cover","domain":"Theoretical computer science","family":"102","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"cs.CC","summary":"We prove that minimum Vertex Cover is NP-hard to approximate within every fixed factor below two, even on simple unweighted graphs.","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"The Unique Games Conjecture and optimal approximation thresholds"}