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Ramsey Online Game developed by J.A Grytczuk and M. Haluszxzak and also Jozsef Balogh and Jane Buterfield based on knowledge of Ramsey Numbers. Given positive integer m and n, we want to find the smallest integer r= r(m,n) such that if edges of complete graph Kr with r arbitrary vertices color with...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/16107 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Ramsey Online Game developed by J.A Grytczuk and M. Haluszxzak and also Jozsef Balogh and Jane Buterfield based on knowledge of Ramsey Numbers. Given positive integer m and n, we want to find the smallest integer r= r(m,n) such that if edges of complete graph Kr with r arbitrary vertices color with 2-coloured (red and blue) then sub graph red Km or blue Km appears. In other words, for every arbitrary graph F with r vertices: F has red Km or complement of F has Km as sub graph. <br />
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Ramsey Online Games played on unbounded set of vertices. There are two players, Builder and Painter. On each move, Builder shows an edge then Painter colored it. The goal is to force Painter make graph H. The main problem of this game is to recognize the winner if given vertices and graph H. Graph H in this final project is a cycle. <br />
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On this final project, we investigate the game strategy and make Ramsey Online Games. |
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