Ramsey number of fans [article]

Guantao Chen, Xiaowei Yu, Yi Zhao
<span title="2020-06-30">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For a given graph H, the Ramsey number r(H) is the minimum N such that any 2-edge-coloring of the complete graph K_N yields a monochromatic copy of H. Given a positive integer n, let nK_3, F_n and B_n be three graphs formed by n triangles that share zero, one, and two common vertices, respectively. Burr, Erdős and Spencer in 1975 showed that r(nK_3) = 5n for n > 2. Rousseau and Sheehan in 1978 showed that r(B_n)< 4n + 2 and equality holds for infinitely many values of n. We believe that r(B_n)<
more &raquo; ... r(F_n)< r(n K_3) for sufficiently large n. We confirm the first inequality by showing that 9n/2-5< r(F_n)<11n/2 + 6 for any n. This improves previously known bounds 4n+2 < r(F_n)< 6n.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.00152v1">arXiv:2007.00152v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mnipdfx3zrbhtnrg35lb3yante">fatcat:mnipdfx3zrbhtnrg35lb3yante</a> </span>
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