The Ramsey number for a cycle of length six versus a clique of order eight

Yaojun Chen; Edwin Tai Chiu Cheng; Ran Xu

doi:10.1016/j.dam.2008.04.014

The Ramsey number for a cycle of length six versus a clique of order eight

Yaojun Chen, Edwin Tai Chiu Cheng, Ran Xu

Research output: Journal article publication › Journal article › Academic research › peer-review

3 Citations (Scopus)

Abstract

For two given graphs G1and G2, the Ramsey number R (G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1or the complement of G contains G2. Let Cmdenote a cycle of length m and Kna complete graph of order n. In this paper, it is shown that R (C6, K8) = 36.

Original language	English
Pages (from-to)	8-12
Number of pages	5
Journal	Discrete Applied Mathematics
Volume	157
Issue number	1
DOIs	https://doi.org/10.1016/j.dam.2008.04.014
Publication status	Published - 6 Jan 2009

Keywords

Complete graph
Cycle
Ramsey number

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

More information

10.1016/j.dam.2008.04.014

Cite this

@article{cf441bcede154f4ebe54caf0faf90fe7,

title = "The Ramsey number for a cycle of length six versus a clique of order eight",

abstract = "For two given graphs G1and G2, the Ramsey number R (G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1or the complement of G contains G2. Let Cmdenote a cycle of length m and Kna complete graph of order n. In this paper, it is shown that R (C6, K8) = 36.",

keywords = "Complete graph, Cycle, Ramsey number",

author = "Yaojun Chen and Cheng, {Edwin Tai Chiu} and Ran Xu",

year = "2009",

month = jan,

day = "6",

doi = "10.1016/j.dam.2008.04.014",

language = "English",

volume = "157",

pages = "8--12",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - The Ramsey number for a cycle of length six versus a clique of order eight

AU - Chen, Yaojun

AU - Cheng, Edwin Tai Chiu

AU - Xu, Ran

PY - 2009/1/6

Y1 - 2009/1/6

N2 - For two given graphs G1and G2, the Ramsey number R (G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1or the complement of G contains G2. Let Cmdenote a cycle of length m and Kna complete graph of order n. In this paper, it is shown that R (C6, K8) = 36.

AB - For two given graphs G1and G2, the Ramsey number R (G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1or the complement of G contains G2. Let Cmdenote a cycle of length m and Kna complete graph of order n. In this paper, it is shown that R (C6, K8) = 36.

KW - Complete graph

KW - Cycle

KW - Ramsey number

UR - http://www.scopus.com/inward/record.url?scp=56649094480&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2008.04.014

DO - 10.1016/j.dam.2008.04.014

M3 - Journal article

SN - 0166-218X

VL - 157

SP - 8

EP - 12

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 1

ER -

The Ramsey number for a cycle of length six versus a clique of order eight

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this