The Ramsey number of loose cycles versus cliques |
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Authors: | Arès Méroueh |
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Institution: | Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Cambridge, UK |
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Abstract: | Let be the Ramsey number of an -uniform loose cycle of length versus an -uniform clique of order . Kostochka et al. showed that for each fixed , the order of magnitude of is up to a polylogarithmic factor in . They conjectured that for each we have . We prove that , and more generally for every that . We also prove that for every and , if is odd, which improves upon the result of Collier-Cartaino et al. who proved that for every and we have . |
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Keywords: | loose cycle Ramsey number |
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