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 -