这样,Erdős–Szekeres定理可以重新表述为: Theorem (Erdős–Szekeres): (S,≺) 为偏序集 m,n∈N+, |S|=mn+1 ,那么 S 存在长为 m+1 的链或长为 n+1 的反链。 下面证明Dilworth定理: Lemma (Dilworth): 偏序集最少的链划分数等于其最长反链长度。proof: 对偏序集 (S,≺) 的元素个数 m进行...
According to the Erd\\H{o}s-Szekeres theorem, for every n, a sufficiently large set of points in the plane contains n in convex position. In this note we investigate the line version of this result, that is, we want to find n lines in convex position in a sufficiently large set of...
While it is unecessary to prove the following theorem in order to prove Ramsey’s theorem for hypergraphs in r colors (which is the form of the theorem we use inthe proof of the Erd˝os-Szekeres theorem),we present this proof to familiarize the reader with Ramsey’s theorem in a simpler...
In this note we discuss some extensions of this theorem and show how they can be used to proof several other results in hamiltonian graph theory. Although several of the results are known, the proofs in this note are in general essentially shorter than the original proofs, and also give an...
According to the ErdAs-Szekeres theorem, for every n, a sufficiently large set of points in general position in the plane contains n in convex position. In this note we investigate the line version of this result, that is, we want to find n lines in convex position in a sufficiently ...
According to the classical Erdős–Szekeres theorem, every sufficiently large set of points in general position in the plane contains a large subset in convex position. Parallel to the Erdős–Hajnal problem in graph-Ramsey theory, we investigate how large such subsets must a configuration ...
We prove a fractional version of the Erds—Szekeres theorem: for any k there is a constant c k > 0 such that any sufficiently large finite set X R 2 contains k subsets Y 1 , ... ,Y k , each of size ≥ c k |X| , such that every set {y 1 ,...,y k } with y i ε ...
A one-dimensional analog of Theorem 2 is a reformulation of a known theorem concerning intervals on the real line.doi:10.1016/0012-365X(90)90232-7A. BialostockiP. DierkerB. VoxmanDiscrete MathematicsA. Bialostocki, P. Dierker and B. Voxman, “Some notes on the Erdős-Szekeres theorem...
order typeRamsey theoryErdos-Szekeres conjecturecombinatorial convexityRAMSEY-TYPE THEOREMSAccording to the classical Erdos-Szekeres theorem, every sufficiently large set of points in general position in the plane contains a large subset in convex position. Parallel to the Erdos-Hajnal problem in graph-...
A Generalization of the Erdos-Szekeres Theorem to disjoint Convex Sets[J].Discrete and Computational Geometry,1998.437-445.doi:10.1007/PL00009361.J Pach. A generalization of the Erdos-Szekeres theorem to disjoint convex sets[J].Discrete and Computational Geometry,1998,(19):437-445.doi:10.1007/PL...