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mmr 2021, 7(4): 714-726 |
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Maherani L, Omidi G. Around a conjecture of Erdos in graph Ramsey theory. mmr 2021; 7 (4) :714-726
URL: http://mmr.khu.ac.ir/article-1-2877-en.html
URL: http://mmr.khu.ac.ir/article-1-2877-en.html
1- Isfahan University of technology , l.maherani@math.iut.ac.ir
2- Isfahan University of technology and (IPM)
2- Isfahan University of technology and (IPM)
Abstract: (672 Views)
For given graphs G1 and G2 the Ramsey number R(G1;G2), is the smallest positive
integer n such that each blue-red edge coloring of the complete graph Kn contains a blue
copy of G1 or a red copy of G2. In 1983, Erd}os conjectured that there is an absolute constant
c such that R(G) = R(G;G) 2c
p
m for any graph G with m edges and no isolated vertices.
Recently this conjecture was proved by Sudakov. In this short note, we give an extention
of this result. As a corollary of our result we have R(G1;G2) 2250
p
m for graphs G1 and
G2 with no isolated vertices and m1 and m2 edges, respectively, where m = fm1;m2g
Keywords: Ramsey number, Erd}os' conjecrure.
integer n such that each blue-red edge coloring of the complete graph Kn contains a blue
copy of G1 or a red copy of G2. In 1983, Erd}os conjectured that there is an absolute constant
c such that R(G) = R(G;G) 2c
p
m for any graph G with m edges and no isolated vertices.
Recently this conjecture was proved by Sudakov. In this short note, we give an extention
of this result. As a corollary of our result we have R(G1;G2) 2250
p
m for graphs G1 and
G2 with no isolated vertices and m1 and m2 edges, respectively, where m = fm1;m2g
Keywords: Ramsey number, Erd}os' conjecrure.
Type of Study: Original Manuscript |
Subject:
alg
Received: 2018/11/14 | Revised: 2023/06/18 | Accepted: 2020/05/30 | Published: 2022/03/29 | ePublished: 2022/03/29
Received: 2018/11/14 | Revised: 2023/06/18 | Accepted: 2020/05/30 | Published: 2022/03/29 | ePublished: 2022/03/29
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