组合数学 (Fall 2024)/Ramsey theory: Revision history

29 May 2024

• curprev 12:1412:14, 29 May 2024‎ Etone talk contribs‎ 26,029 bytes +26,029‎ Created page with "== Ramsey's Theorem == === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem| :Let <math>k,\ell</math> be positive integers. Then there exists an integer <math>R(k,\ell)</math> satisfying: :If <math>n\ge R(k,\ell)</math>, for any coloring of edges of <math>K_n</math> with two colors red and blue, there exists a red <math>K_k</math> or a blue <math>K_\ell</math>. }} {{Proof| We show that <math>R(k,\ell)</math> is finite by induction on <math>k+\ell</math>. For the..."