On Star–Wheel Ramsey Numbers

被引：0
作者：
Binlong Li
Ingo Schiermeyer
机构：
[1] Northwestern Polytechnical University,Department of Applied Mathematics
[2] University of West Bohemia,European Centre of Excellence NTIS
[3] Technische Universität Bergakademie Freiberg,Institut für Diskrete Mathematik und Algebra
来源：
Graphs and Combinatorics | 2016年 / 32卷
关键词：
Ramsey number; Star; Wheel; 05C55; 05D10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For two given graphs G1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_1$$\end{document} and G2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_2$$\end{document}, the Ramsey number R(G1,G2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R(G_1,G_2)$$\end{document} is the least integer r such that for every graph G on r vertices, either G contains a G1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_1$$\end{document} or G¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{G}$$\end{document} contains a G2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_2$$\end{document}. In this note, we determined the Ramsey number R(K1,n,Wm)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R(K_{1,n},W_m)$$\end{document} for even m with n+2≤m≤2n-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n+2\le m\le 2n-2$$\end{document}, where Wm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W_m$$\end{document} is the wheel on m+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m+1$$\end{document} vertices, i.e., the graph obtained from a cycle Cm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_m$$\end{document} by adding a vertex v adjacent to all vertices of the Cm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_m$$\end{document}.
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页码：733 / 739
页数：6
相关论文
共 17 条
[1]  
Brandt S(1998)Weakly pancyclic graphs J. Graph Theory 27 141-176
[2]  
Faudree RJ(2004)The Ramsey numbers of stars versus wheels Eur. J. Comb. 25 1067-1075
[3]  
Goddard W(1952)Some theorems on abstract graphs Proc. Lond. Math. Soc. 2 69-81
[4]  
Chen Y(2005)Star–wheel Ramsey numbers J. Comb. Math. Comb. Comput. 55 123-128
[5]  
Zhang Y(1981)Cycles in bipartite graphs J. Comb. Theory Ser. B 30 332-342
[6]  
Zhang K(2008)The Ramsey numbers for stars of even order versus a wheel of order nine Eur. J. Comb. 29 1744-1754
[7]  
Dirac GA(2009)The Ramsey numbers for stars of odd order versus a wheel of order nine Discrete Math. Algorithm Appl. 1 413-436
[8]  
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[9]  
Baskoro ET(undefined)undefined undefined undefined undefined-undefined
[10]  
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