#TITLE_ALTERNATIVE#
Graph G is a nonempty set V(G) of vertices and a set E(G) of edges. For any positive integer m,n, a ramsey number r(m,n) is the least integer r such that for any red-blue coloring on the edges of complete graph Kr on r vertices there always exists either a red complete graph Km or a blue complete gr...
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| Main Author: | |
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/15776 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Graph G is a nonempty set V(G) of vertices and a set E(G) of edges. For any positive integer m,n, a ramsey number r(m,n) is the least integer r such that for any red-blue coloring on the edges of complete graph Kr on r vertices there always exists either a red complete graph Km or a blue complete graph Kn as a subgraph. For certain graphs F, G and H, notation of F -> (G,H) means that if any red-blue coloring on the edges of F, there will occur a red subgraph G or a blue subgraph H on F. A (G,H)-coloring is a 2-coloring (red-blue coloring) if neither a red G nor a blue H occurs. Graph F is Ramsey (G,H)-minimal if for any redblue edge coloring of F, there exists a red subgraph G or a blue subgraph H on F and there exists a redblue coloring on F-{e}, for any edge e, such that neither a red subgraph G nor a blue subgraph H occurs. Let R(G,H) be the class consists of all Ramsey (G,H)-minimal graph. In this final project, we investigate the class R(P3,H). We will give a number of graphs which are in this ramsey minimal set. |
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