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- W2012415754 abstract "We prove a partitioned version of the Erdös–Szekeres theorem for the case $k = 4$: any finite set $X subset bbbr^2$ of points in general position can be partitioned into sets $X_0, X_{ij}$ where $i=1,2,3,4$ and $j=1,ldots,26$, so that $|X_{1j}|=|X_{2j}|=|X_{3j}|=|X_{4j}|$, $|X_0|leq 4$ and for all $j$ every transversal ${x_1,x_2,x_3,x_4}$, $x_1 in X_{1j}, x_2 in X_{2j},x_3 in X_{3j}, x_4 in X_{4j}$, is in convex position. In order to prove this, we show another theorem, the partitioned version of the “same type lemma”, which was proved by Bárány and Valtr." @default.
- W2012415754 created "2016-06-24" @default.
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- W2012415754 date "2003-08-01" @default.
- W2012415754 modified "2023-09-23" @default.
- W2012415754 title "A Partitioned Version of the Erd�s?Szekeres Theorem for Quadrilaterals" @default.
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- W2012415754 doi "https://doi.org/10.1007/s00454-003-0013-8" @default.
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