Question
This theorem gave rise to a branch of combinatorics that studies how order emerges as system size grows. For 10 points each:
[10m] Name this theorem which states that coloring a graph with R(s, t) (“R-of-s-comma-t”) vertices will create a monochromatic complete subgraph of size s or of size t.
ANSWER: Ramsey’s theorem [accept Ramsey theory]
[10e] This Hungarian mathematician and George Szekeres (“SEH-keh-resh”) established an upper bound for the Ramsey number. This mathematician’s namesake number is the publishing distance between him and someone else.
ANSWER: Paul Erdős (“AIR-dish”) [or Erdős Pál]
[10h] Van der Waerden’s (“VAN der VAR-din’s”) theorem in Ramsey theory is a precursor to this theorem. This theorem states that any subset of the positive integers of positive upper density contains arbitrarily long arithmetic (“air-ith-MET-ick”) progressions.
ANSWER: Szemerédi's (“SEH-meh-ray-dee’s”) theorem [reject “Szemerédi regularity lemma”]
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