THE CYCLE-COMPLETE GRAPH RAMSEY NUMBER r(C5;K9) - IMANSYAH YAHYA (20114052), NISKY
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 → (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 number r(G,H) is the minimum number of vertices of graph F such that F → (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 α(G) ≥ 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 ≥ n ≥ 3 except r(C3,K3) = 6. In this thesis we will present a proof that cycle-complete graph Ramsey number r(C5,K9) = 33.