THE RAMSEY NUMBER FOR THETA GRAPH VERSUS A CLIQUE OF ORDER THREE AND FOUR

被引：3

作者：

Bataineh, M. S. A. ^{[1
]}

Jaradat, M. M. M. ^{[2
]}

Bateeha, M. S. ^{[1
]}

机构：

[1] Yarmouk Univ, Dept Math, Irbid, Jordan

[2] Quatar Univ, Dept Math Stat & Phys, Doha, Qatar

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2014年 / 34卷 / 02期

关键词：

Ramsey number; independent set; theta graph; complete graph;

D O I：

10.7151/dmgt.1730

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For any two graphs F-1 and F-2 the graph Ramsey number r(F-1, F-2) is the smallest positive integer N with the property that every graph on at least N vertices contains F-1 or its complement contains F-2 as a subgraph. In this paper, we consider the Ramsey numbers for theta-complete graphs. We determine r(theta(n), K-m) for m = 2,3,4 and n > m. More specifically, we establish that r(theta(n), K-m) = (n - 1)(m - 1) + 1 for m = 3,4 and n> m.

引用

页码：223 / 232

页数：10

共 8 条

[1]

Bolze R., 1981, THEORY APPL GRAPHS, P109

[2]

Boza L., 2010, P 7 JORN MAT DISCR A

[3] GENERALIZED RAMSEY THEORY FOR GRAPHS .3. SMALL OFF-DIAGONAL NUMBERS [J].