The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers

Yusheng Li and Wenan Zang ()
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Yusheng Li: Tongji University
Wenan Zang: Tongji University

Journal of Combinatorial Optimization, 2003, vol. 7, issue 4, No 3, 353-359

Abstract: 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.

Keywords: independence number; Ramsey number; probabilistic method; graph coloring (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/B:JOCO.0000017383.13275.17

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