Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking
Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking
复制标题
使用抽象和对称性破缺计算拉姆齐数 R(4,3,3)
DOI：
10.1007/s10601-016-9240-3
复制
发表时间：
2015
期刊：
影响因子：
1.6
通讯作者：
Alice Miller
中科院分区：
文献类型：
--
作者：
M. Codish;Michael Frank;Avraham Itzhakov;Alice Miller
数字R(4，3，3)通常被表示为未知的Ramsey数，最有可能“很快”被发现。然而，近50年来，它的确切价值一直不得而知。本文提出了一种基于抽象和对称破缺的方法来解决硬图的边着色问题。通过计算R(4，3，3)=30的值，说明了该方法的实用性。在此过程中，需要首先计算以前未知的集合ℛ(3，3，3；13)\DocumentClass[12pt]{Minimum}\Usepackage{amsath}\usepackage{waysym}\usepackage{amsFonts}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setLong{\oddsidemargin}{-69pt}\Begin{Document}$\mathcal{R}(3，3，3；13)$\end{Document}，其中包含78,892个Ramsey颜色。
The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found “soon”. Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on abstraction and symmetry breaking that applies to solve hard graph edge-coloring problems. The utility of this methodology is demonstrated by using it to compute the value R(4, 3, 3) = 30. Along the way it is required to first compute the previously unknown set ℛ(3,3,3;13)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {R}(3,3,3;13)$\end{document} consisting of 78,892 Ramsey colorings.
影响因子：
1.6
作者：
Codish M
通讯作者：
Codish M