ON THE RESTRICTED SIZE RAMSEY NUMBER OF STARS VERSUS WHEELS WITH 5 OR 6 VERTICES
Given graphs G and H, write F →(G,H), if in any 2-coloring (red and blue)of the edges of F there is a copy of G in red color or a copy of H in blue color.Ramsey number r(G,H) is the smallest integer n such that Kn →(G,H). The size Ramsey number ^r(G,H) is min{|E(F)|:F →...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/22238 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Given graphs G and H, write F →(G,H), if in any 2-coloring (red and blue)of the edges of F there is a copy of G in red color or a copy of H in blue color.Ramsey number r(G,H) is the smallest integer n such that Kn →(G,H). The size Ramsey number ^r(G,H) is min{|E(F)|:F →(G,H)}. Restricted size Ramsey number r*(G,H) is min{|E(F)| : F → (G,H),|V(F)| = r(G,H)|. This thesis intention is to obtain lower bound and upper bound of restricted size Ramsey number for stars versus wheels with 5 or 6 vertices, that is for n ≥ 2, n2 + n ≤ r(K1,n,W4) ≤ 2n2 + n if n even, n2 + n ≤ r*(K1,n,W4) ≤ 2n2+5n+3 if n odd and 3n2 ≤ r*(K1,n,W5)≤ (9n2+3n)/2. |
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