TY - GEN

T1 - Restricted size Ramsey number for P 3 versus dense connected graphs of order six

AU - Silaban, D. R.

AU - Baskoro, E. T.

AU - Uttunggadewa, S.

N1 - Funding Information:
This research is funded by Universitas Indonesia with PITTA 2016 research grant scheme.
Publisher Copyright:
© 2017 Author(s).

PY - 2017/7/10

Y1 - 2017/7/10

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 min {v(F): F → (G, H)}, the size Ramsey number r∗(G, H) is min {e(F): F → (G, H)}, and the restricted size Ramsey number r∗(G, H) is min {e(F): F → (G, H), v(F) = r(G, H)}. In 1972, Chvá tal and Harary gave the Ramsey number for P3 versus any graph H with no isolates. In 1983, Harary and Miller started the investigation of the (restricted) size Ramsey number for some pairs of small graphs with order at most four. In 1983, Faudree and Sheehan continued the investigation and summarized the complete results on the (restricted) size Ramsey number for all pairs of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for all pairs of small forests with order at most five. Lately, we investigate the restricted size Ramsey number for a path of order three versus all connected graphs of order five. In this work, we continue the investigation on the restricted size Ramsey number for a pair of small graphs. In particularly, for a path of order three versus connected graphs of order six.

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 min {v(F): F → (G, H)}, the size Ramsey number r∗(G, H) is min {e(F): F → (G, H)}, and the restricted size Ramsey number r∗(G, H) is min {e(F): F → (G, H), v(F) = r(G, H)}. In 1972, Chvá tal and Harary gave the Ramsey number for P3 versus any graph H with no isolates. In 1983, Harary and Miller started the investigation of the (restricted) size Ramsey number for some pairs of small graphs with order at most four. In 1983, Faudree and Sheehan continued the investigation and summarized the complete results on the (restricted) size Ramsey number for all pairs of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for all pairs of small forests with order at most five. Lately, we investigate the restricted size Ramsey number for a path of order three versus all connected graphs of order five. In this work, we continue the investigation on the restricted size Ramsey number for a pair of small graphs. In particularly, for a path of order three versus connected graphs of order six.

UR - http://www.scopus.com/inward/record.url?scp=85026216426&partnerID=8YFLogxK

U2 - 10.1063/1.4991240

DO - 10.1063/1.4991240

M3 - Conference contribution

AN - SCOPUS:85026216426

T3 - AIP Conference Proceedings

BT - International Symposium on Current Progress in Mathematics and Sciences 2016, ISCPMS 2016

A2 - Sugeng, Kiki Ariyanti

A2 - Triyono, Djoko

A2 - Mart, Terry

PB - American Institute of Physics Inc.

T2 - 2nd International Symposium on Current Progress in Mathematics and Sciences 2016, ISCPMS 2016

Y2 - 1 November 2016 through 2 November 2016

ER -