Some Tree-book Ramsey Numbers

被引：0

作者：

Zhang, Lianmin ^{[1
]}

Chen, Kun ^{[2
]}

Zhu, Dongmei ^{[3
]}

机构：

[1] Nanjing Univ, Sch Management & Engn, Nanjing, Jiangsu, Peoples R China

[2] Southwestern Univ Finance & Econ, Sch Stat, Chengdu, Peoples R China

[3] Southeast Univ, Sch Econ & Management, Nanjing, Jiangsu, Peoples R China

来源：

ARS COMBINATORIA | 2017年 / 130卷

基金：

中国国家自然科学基金;

关键词：

Ramsey number; Tree; Book;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For two given graphs G(1) and G(2), the Ramsey number R(G(1), G(2)) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. In this paper, we study a large class of tree T as studied by Cockayne in [3], including paths, trees which have a vertex of degree one adjacent to vertex of degree two, as special cases. We evaluate some R(T`(m),B-m), where T`(n) is an element of T and B-m, is a book of order m+2. Besides, some bounds for R(T`(n) ,B-m) are obtained.

引用

页码：97 / 102

页数：6

共 9 条

[1]

[Anonymous], 1952, Proceedings of the London Mathematical Society, DOI [10.1112/plms/s3-2.1.69, DOI 10.1112/PLMS/S3-2.1.69]

[2]

Burr S.A., 1974, UTILITAS MATHEMATICA, V4, P217

[3]

Chartrand G., 1981, THOERY APPL GRAPHS, P203

[4]

Cockayne E., 1974, J COMBINATORIAL THEO, V17, P183

[5]

Erdos P., 1988, SCI A, V1, P111

[6] On book-complete graph Ramsey numbers [J].

Li, YS ;

Rousseau, CC .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1996, 68 (01) :36-44

[7]

Radziszowski S.P., 2014, ELECT J COMBINATORIC

[8]

Rousseau C.C., 1978, J. Graph Theory, V2, P77

[9]

ROUSSEAU CC, 1978, J LOND MATH SOC, V18, P392

← 1 →