THE CYCLE-COMPLETE GRAPH RAMSEY NUMBER r(C5;K9)

• Main Author: IMANSYAH YAHYA (20114052), NISKY
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/23511
• Institution: Institut Teknologi Bandung

The problem finding Ramsey number graphs is one of the problems developed from the classical Ramsey theory. Let F; G; and H be nonempty graphs. We write F &#8594; (G,H) means that any red-blue coloring of the edge of F, then F contains a red subgraph G or F contains a blue subgraph H. The Ramsey <br /> <br /> <br /> number r(G,H) is the minimum number of vertices of graph F such that F &#8594; (G,H). The cycle-complete graph Ramsey number r(Cm,Kn) is the smallest integer N such that every graph G of order N contains a cycle Cm on m vertices or has independence number &#945;(G) &#8805; n. The finding of cycle-complete graph Ramsey number has been conjectured by Erdos, Faudree, Rousseau and Schelp that r(Cm,Kn) = (m - 1)(n - 1) + 1 for all m &#8805; n &#8805; 3 except r(C3,K3) = 6. In this thesis we will present a proof that cycle-complete graph Ramsey number <br /> <br /> <br /> r(C5,K9) = 33.