An Exact Formula for all Star-Kipas Ramsey Numbers

详细信息    查看全文

• 作者：Binlong Li ; Yanbo Zhang ; Hajo Broersma
• 关键词：Ramsey number ; Star ; Kipas ; Wheel
• 刊名：Graphs and Combinatorics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：141-148
• 全文大小：357KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Engineering Design;
• 出版者：Springer Japan
• ISSN：1435-5914
• 卷排序：33

文摘

Let \(G_1\) and \(G_2\) be two given graphs. The Ramsey number \(R(G_1,G_2)\) is the least integer r such that for every graph G on r vertices, either G contains a \(G_1\) or \(\overline{G}\) contains a \(G_2\). A complete bipartite graph \(K_{1,n}\) is called a star. The kipas \(\widehat{K}_n\) is the graph obtained from a path of order n by adding a new vertex and joining it to all the vertices of the path. Alternatively, a kipas is a wheel with one edge on the rim deleted. Whereas for star-wheel Ramsey numbers not all exact values are known to date, in contrast we determine all exact values of star-kipas Ramsey numbers.