TY - GEN
T1 - Restricted size Ramsey number for P 3 versus small paths
AU - Silaban, Denny Riama
AU - Baskoro, E. T.
AU - Uttunggadewa, Saladin
N1 - Publisher Copyright:
© 2016 AIP Publishing LLC.
PY - 2016/2/11
Y1 - 2016/2/11
N2 - Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exist a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min {|V (F)|: F → (G, H)}, the size Ramsey number r(G, H) is defined as min {|E(F)|: F → (G, H)}, and the restricted size Ramsey number r∗(G, H) is defined as min {|E(F)|: F → (G, H), |V (F)| = r(G, H)}. In this paper we give a lower bound for the restricted size Ramsey number for a path P3 versus Pn. We also give the upper bound and the exact restricted size Ramsey number for some small values of n.
AB - Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exist a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min {|V (F)|: F → (G, H)}, the size Ramsey number r(G, H) is defined as min {|E(F)|: F → (G, H)}, and the restricted size Ramsey number r∗(G, H) is defined as min {|E(F)|: F → (G, H), |V (F)| = r(G, H)}. In this paper we give a lower bound for the restricted size Ramsey number for a path P3 versus Pn. We also give the upper bound and the exact restricted size Ramsey number for some small values of n.
UR - http://www.scopus.com/inward/record.url?scp=84984555020&partnerID=8YFLogxK
U2 - 10.1063/1.4940821
DO - 10.1063/1.4940821
M3 - Conference contribution
AN - SCOPUS:84984555020
T3 - AIP Conference Proceedings
BT - Proceedings of the 7th SEAMS UGM International Conference on Mathematics and Its Applications 2015
A2 - Susanti, Yeni
A2 - Wijayanti, Indah Emilia
A2 - Kusumo, Fajar Adi
A2 - Aluicius, Irwan Endrayanto
PB - American Institute of Physics Inc.
T2 - 7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research
Y2 - 18 August 2015 through 21 August 2015
ER -