The graph Ramsey number R(Fl, K6)

被引：3

作者：

Kadota, Shin-Ya ^{[1
]}

Onozuka, Tomokazu ^{[2
]}

Suzuki, Yuta ^{[3
]}

机构：

[1] Niihama Coll, Natl Inst Technol, Yagumocho, Ehime 7928580, Japan

[2] Kyushu Univ, Multiple Zeta Res Ctr, Nishi Ku, Fukuoka, Fukuoka 8190395, Japan

[3] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

来源：

DISCRETE MATHEMATICS | 2019年 / 342卷 / 04期

关键词：

Ramsey number; Fan graph; Complete graph;

D O I：

10.1016/j.disc.2018.12.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a given pair of two graphs (F, H), let R(F, H) be the smallest positive integer r such that for any graph G of order r, either G contains F as a subgraph or the complement of G contains H as a subgraph. Baskoro, Broersma and Surahmat (2005) conjectured that R(F-l, K-n) = 2l(n - 1) + 1 for l >= n >= 3, where F-l is the join K-1 + lK(2) of K-1 and lK(2). In this paper, we prove that this conjecture is true for the case n = 6. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：1028 / 1037

页数：10

共 8 条

[1]

Baskoro Surahmat ET., 2005, B I COMBIN APPL, V43, P96

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

CHVATAL, V ;

HARARY, F .

PACIFIC JOURNAL OF MATHEMATICS, 1972, 41 (02) :335-&

[3]

Diestel Reinhard, 2010, GRAPH THEORY, V4th

[4]

Gupta S.K., 1997, J COMB, V22, P85

[5]

Li YS, 1996, J GRAPH THEOR, V23, P413, DOI 10.1002/(SICI)1097-0118(199612)23:4<413::AID-JGT10>3.0.CO

[6]

2-D

[7] RAMSEY NUMBER R(F,KM) WHERE F IS A FOREST [J].

STAHL, S .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1975, 27 (03) :585-589

[8] The Ramsey numbers of fans versus a complete graph of order five [J].

Zhang, Yanbo ;

Chen, Yaojun .

ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS, 2014, 2 (01) :66-69

← 1 →