TY - JOUR

T1 - Restricted Size Ramsey Number for 2K2 versus Dense Connected Graphs of Order Six

AU - Silaban, Denny Riama

AU - Baskoro, Edy Tri

AU - Uttunggadewa, Saladin

N1 - Publisher Copyright:
© Published under licence by IOP Publishing Ltd.

PY - 2018/4/27

Y1 - 2018/4/27

N2 - Let G and H be simple graphs. The Ramsey number r(G, H) for a pair of graphs G and H is the smallest number r such that any red-blue coloring of the edges of Kr contains a red subgraph G or a blue subgraph H. The size Ramsey number for a pair of graphs G and H is the smallest number such that there exists a graph F with size satisfying the property that any red-blue coloring of the edges of F contains a red subgraph G or a blue subgraph H. Additionally, if the order of F in the size Ramsey number equals r(G, H), then it is called the restricted size Ramsey number. In 1972, Chvátal and Harary gave the Ramsey number for 2K 2 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 2K 2 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 2K 2 versus dense connected graph of order six.

AB - Let G and H be simple graphs. The Ramsey number r(G, H) for a pair of graphs G and H is the smallest number r such that any red-blue coloring of the edges of Kr contains a red subgraph G or a blue subgraph H. The size Ramsey number for a pair of graphs G and H is the smallest number such that there exists a graph F with size satisfying the property that any red-blue coloring of the edges of F contains a red subgraph G or a blue subgraph H. Additionally, if the order of F in the size Ramsey number equals r(G, H), then it is called the restricted size Ramsey number. In 1972, Chvátal and Harary gave the Ramsey number for 2K 2 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 2K 2 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 2K 2 versus dense connected graph of order six.

UR - http://www.scopus.com/inward/record.url?scp=85047425023&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1008/1/012034

DO - 10.1088/1742-6596/1008/1/012034

M3 - Conference article

AN - SCOPUS:85047425023

SN - 1742-6588

VL - 1008

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012034

T2 - 1st International Conference of Combinatorics, Graph Theory, and Network Topology, ICCGANT 2017

Y2 - 25 November 2017 through 26 November 2017

ER -