EMBEDDINGS AND RAMSEY NUMBERS OF SPARSE k-UNIFORM HYPERGRAPHS
نویسندگان
چکیده
Chvátal, Rödl, Szemerédi and Trotter [3] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [6, 23] the same result was proved for 3-uniform hypergraphs. Here we extend this result to k-uniform hypergraphs for any integer k ≥ 3. As in the 3-uniform case, the main new tool which we prove and use is an embedding lemma for k-uniform hypergraphs of bounded maximum degree into suitable k-uniform ‘quasi-random’ hypergraphs. keywords: hypergraphs; regularity lemma; Ramsey numbers; embedding problems
منابع مشابه
D ec 2 00 6 EMBEDDINGS AND RAMSEY NUMBERS OF SPARSE k - UNIFORM HYPERGRAPHS
Chvátal, Rödl, Szemerédi and Trotter [3] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [5, 19] the same result was proved for 3-uniform hypergraphs. Here we extend this result to k-uniform hypergraphs for any integer k ≥ 3. As in the 3-uniform case, the main new tool which we prove and use is an embedding lemma for k-uniform hypergraphs of boun...
متن کاملRamsey-like cardinals
One of the numerous characterizations of a Ramsey cardinal κ involves the existence of certain types of elementary embeddings for transitive sets of size κ satisfying a large fragment of ZFC. I introduce new large cardinal axioms generalizing the Ramsey elementary embeddings characterization and show that they form a natural hierarchy between weakly compact cardinals and measurable cardinals. T...
متن کاملRamsey-like cardinals II
This paper continues the study of the Ramsey-like large cardinals introduced in [Git09] and [WS08]. Ramsey-like cardinals are defined by generalizing the “existence of elementary embeddings” characterization of Ramsey cardinals. A cardinal κ is Ramsey if and only if every subset of κ can be put into a κ-size transitive model of ZFC for which there exists a weakly amenable countably complete ult...
متن کاملLow dimensional embeddings of ultrametrics
In this note we show that every n-point ultrametric embeds with constant distortion in l O(logn) p for every ∞ ≥ p ≥ 1. More precisely, we consider a special type of ultrametric with hierarchical structure called a k-hierarchically well-separated tree (k-HST). We show that any k-HST can be embedded with distortion at most 1 + O(1/k) in l O(k2 logn) p . These facts have implications to embedding...
متن کاملEfficient Construction of Probabilistic Tree Embeddings
In this paper we describe a simple and efficient algorithm to construct FRT embeddings (optimal probabilistic tree embeddings) on graphs. For a graph with n vertices and m edges the algorithm runs in O(m log n + n log n) time. With the efficient FRT construction, we show that FRT trees are Ramsey partitions with asymptotically tight bound, and we give tighter bounds on coefficient than previous...
متن کامل