Configurations in projective planes and quadrilateral-star Ramsey numbers

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• 作者：E.L. Monte Carmelo
• 关键词：Generalized Ramsey number ; Projective plane ; Polarity ; Star ; Four-cycle
• 刊名：Discrete Mathematics
• 出版年：2008
• 出版时间：6 September 2008
• 年：2008
• 卷：308
• 期：17
• 页码：3986-3991
• 全文大小：145 K

文摘

Some classes of configurations in projective planes with polarity are constructed. As the main result, lower bounds for the Ramsey numbers r(n)=r(C₄;K_1,n) are derived from these geometric structures, which improve some bounds due to Parsons about 30 years ago, and also yield a new class of optimal values: r(q²-2q+1)=q²-q+1 whenever q is a power of 2. Moreover, the constructions also imply a known result on C₄-K_1,n bipartite Ramsey numbers.