RAMSEY (3K2;K1;n)-MINIMAL GRAPHS
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...
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| Format: | Theses |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/37147 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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