Abstract
Let k ≥ 5 be a fixed integer and let m = ⌊(k − 1)/2⌋. It is shown that the independence number of a C k-free graph is at least c 1[∑ d(v)1/(m − 1)](m − 1)/m and that, for odd k, the Ramsey number r(C k, K n) is at most c 2(n m + 1/log n)1/m, where c 1 = c 1(m) > 0 and c 2 = c 2(m) > 0.
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Li, Y., Zang, W. The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers. Journal of Combinatorial Optimization 7, 353–359 (2003). https://doi.org/10.1023/B:JOCO.0000017383.13275.17
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DOI: https://doi.org/10.1023/B:JOCO.0000017383.13275.17