On the Ramsey numbers of daisies I

Combinatorics, Probability and Computing Pub Date : 2024-09-18 DOI:10.1017/s0963548324000221

Pavel Pudlák, Vojtech Rödl, Marcelo Sales

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引用次数: 0

Abstract

Daisies are a special type of hypergraph introduced by Bollobás, Leader and Malvenuto. An

$r$

-daisy determined by a pair of disjoint sets

$K$

and

$M$

is the

$(r+|K|)$

-uniform hypergraph

$\{K\cup P\,{:}\, P\in M^{(r)}\}$

. Bollobás, Leader and Malvenuto initiated the study of Turán type density problems for daisies. This paper deals with Ramsey numbers of daisies, which are natural generalisations of classical Ramsey numbers. We discuss upper and lower bounds for the Ramsey number of

$r$

-daisies and also for special cases where the size of the kernel is bounded.

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关于拉姆齐雏菊的数量 I

雏形是波尔洛巴斯、利德和马尔维努托提出的一种特殊类型的超图。由一对不相交的集合 $K$ 和 $M$ 决定的 $r$ -雏形是 $(r+|K|)$ -均匀超图 $\{K\cup P\,{:}\, P\in M^{(r)}\}$ 。Bollobás、Leader 和 Malvenuto 发起了对菊花的 Turán 类型密度问题的研究。本文讨论的是雏菊的拉姆齐数，它是经典拉姆齐数的自然概括。我们讨论了 $r$ 雏菊的拉姆齐数的上界和下界，以及内核大小有界的特殊情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorics, Probability and Computing

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