RAMSEY (3K2;K1;n)-MINIMAL GRAPHS - Muhshi, Hadi
For any given graphs G and H, notation F ! (G;H) means that for any red-blue coloring on edges of graph F, a red subgraph G or a blue subgraph H always occur on F. notation F 9 (G;H) means that a red-blue coloring for F such that neither a red subgraph G nor a blue subgraph H occur on F exist. A graph F is called Ramsey (G;H)-minimal graph if F ! (G;H) and F 9 (G;H) for all proper subgraph F of F. Class for all Ramsey (G;H)-minimal graphs is notated by R(G;H). Burr, Erdös, Faudree and Schelp in 1978 proved that R(mK2;H) is finite for any given graph H and positive number m. Then in 1999 Mengersen and Oeckermann gave some characteristics for Ramsey (2K2;K1;n)-minimal graphs for n 3 and gave all Ramsey (2K2;K1;n)-minimal graphs for n 3. In 2012 Muhshi and Baskoro gave all Ramsey (2K2;K1;2)-minimal graphs. Motivated by these results, in this thesis, we find some Ramsey (2K2;K1;n)-minimal graphs and give some characteristics of Ramsey (2K2;K1;n)-minimal graphs for n 3.