@article{ART001976001},
author={Sang-Un, Lee},
title={Experimental Proof for Symmetric Ramsey Numbers},
journal={Journal of The Korea Society of Computer and Information},
issn={1598-849X},
year={2015},
volume={20},
number={3},
pages={69-74}
TY - JOUR
AU - Sang-Un, Lee
TI - Experimental Proof for Symmetric Ramsey Numbers
JO - Journal of The Korea Society of Computer and Information
PY - 2015
VL - 20
IS - 3
PB - The Korean Society Of Computer And Information
SP - 69
EP - 74
SN - 1598-849X
AB - This paper offers solutions to unresolved 43 ≤ R(5,5) ≤ 49and 102 ≤ R(6,6) ≤ 165 problems ofRamsey’s number. The Ramsey’s number R(s,t) of a complete graph Kn dictates that n-1 number ofincidental edges of a arbitrary vertex v is dichotomized into two colors:(n-1)/2=R and (n-1)/2=B .
Therefore, if one introduces the concept of distance to the vertex , one may construct a partite graph Kn = KL + v + KR , to satisfy (n-1)/2=R of {KL,v} and (n-1)/2=B of {v,KR}. Subsequently, given that KL forms the color R of Ks-1 , Ks is attainable. Likewise, given that KR forms the color B of Kt-1 , Kt is obtained. By following the above-mentioned steps, R(s,t) = Kn was obtained, satisfying necessary andsufficient conditions where, for KL and KR , the maximum distance should be even and incidental edges ofall vertices should be equal are satisfied. This paper accordingly proves R(5,5)=43 and R(6,6) = 91.
KW - Ramsey number;Partite graph;Distance;Degree
DO -
UR -
ER -
Sang-Un, Lee. (2015). Experimental Proof for Symmetric Ramsey Numbers. Journal of The Korea Society of Computer and Information, 20(3), 69-74.
Sang-Un, Lee. 2015, "Experimental Proof for Symmetric Ramsey Numbers", Journal of The Korea Society of Computer and Information, vol.20, no.3 pp.69-74.
Sang-Un, Lee "Experimental Proof for Symmetric Ramsey Numbers" Journal of The Korea Society of Computer and Information 20.3 pp.69-74 (2015) : 69.
Sang-Un, Lee. Experimental Proof for Symmetric Ramsey Numbers. 2015; 20(3), 69-74.
Sang-Un, Lee. "Experimental Proof for Symmetric Ramsey Numbers" Journal of The Korea Society of Computer and Information 20, no.3 (2015) : 69-74.
Sang-Un, Lee. Experimental Proof for Symmetric Ramsey Numbers. Journal of The Korea Society of Computer and Information, 20(3), 69-74.
Sang-Un, Lee. Experimental Proof for Symmetric Ramsey Numbers. Journal of The Korea Society of Computer and Information. 2015; 20(3) 69-74.
Sang-Un, Lee. Experimental Proof for Symmetric Ramsey Numbers. 2015; 20(3), 69-74.
Sang-Un, Lee. "Experimental Proof for Symmetric Ramsey Numbers" Journal of The Korea Society of Computer and Information 20, no.3 (2015) : 69-74.
