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Title: | STAR-CRITICAL RAMSEY NUMBERS FOR CYCLES VERSUS K4 |
Authors: | Jayawardene, Chula J. Narvaez, David Radziszowski, Stanis law P. |
Keywords: | Ramsey theory, star-critical Ramsey numbers. |
Issue Date: | 2021 |
Citation: | Jayawardene,C.,Narváez,D. & Radziszowski,S.(2021).Star-Critical Ramsey Numbers for Cycles Versus K4. Discussiones Mathematicae Graph Theory,41(2) 381-390. https://doi.org/10.7151/dmgt.2190 |
Abstract: | Given three graphs G, H and K we write K → (G, H), if in any red/blue coloring of the edges of K there exists a red copy of G or a blue copy of H. The Ramsey number r(G, H) is defined as the smallest natural number n such that Kn → (G, H) and the star-critical Ramsey number r∗(G, H) is defined as the smallest positive integer k such that Kn−1 ⊔ K1,k → (G, H), where n is the Ramsey number r(G, H). When n ≥ 3, we show that r∗(Cn, K4) = 2n except for r∗(C3, K4) = 8 and r∗(C4, K4) = 9. We also characterize all Ramsey critical r(Cn, K4) graphs. |
URI: | https://doi.org/10.7151/dmgt.2190 http://archive.cmb.ac.lk:8080/xmlui/handle/70130/6057 |
Appears in Collections: | Department of Mathematics |
Files in This Item:
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10.7151_dmgt.2190.pdf | 372.46 kB | Adobe PDF | View/Open |
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