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X-WR-CALNAME:Discrete Mathematics Group
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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20250101T000000
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DTSTART;TZID=Asia/Seoul:20260807T150000
DTEND;TZID=Asia/Seoul:20260807T160000
DTSTAMP:20260804T132550Z
CREATED:20260804T132550Z
LAST-MODIFIED:20260804T132550Z
UID:13051-1786114800-1786118400@dimag.ibs.re.kr
SUMMARY:Hyunwoo Lee (이현우)\, A super-exponential lower bound construction for the multicolor triangle Ramsey problem discovered by OpenAI
DESCRIPTION:Let $R_k(3)$ denote the smallest integer $N$ such that every $k$-edge-coloring of the complete graph $K_N$ contains a monochromatic triangle. A simple inductive argument gives the classical factorial upper bound $R_k(3)\leq k!=k^{O(k)}$\, whereas the best previously known lower bound was only exponential in $k$\, namely\, $R_k(3)\geq 2^{\Omega(k)}$. It was a longstanding open problem of Erd\H{o}s whether $R_k(3)$ grows exponentially or super-exponentially in $k$. \nOn August 1\, 2026\, OpenAI\, using an internal AI model\, discovered a construction establishing the super-exponential lower bound $R_k(3)\geq k^{\Omega(k)}$\, thereby resolving Erdős’ longstanding question. In this talk\, I will explain the construction and discuss possible directions for further research\, some of which may already have been explored by other researchers.
URL:https://dimag.ibs.re.kr/event/2026-08-07/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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