A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit <a rel="external noopener" href="https://arxiv.org/pdf/2007.00152v1.pdf">the original URL</a>. The file type is <code>application/pdf</code>.
Ramsey number of fans
[article]
<span title="2020-06-30">2020</span>
<i >
arXiv
</i>
<span class="release-stage" >pre-print</span>
Preserved Fulltext
Other Versions
<span title="2021-05-11">2021</span>
<span class="release-stage">accepted</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2021.103347">doi:10.1016/j.ejc.2021.103347</a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.00152v2">arXiv:2007.00152v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yowqe4rysfbopfmkrdjwuuqyve">fatcat:yowqe4rysfbopfmkrdjwuuqyve</a> </span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2021.103347">doi:10.1016/j.ejc.2021.103347</a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.00152v2">arXiv:2007.00152v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yowqe4rysfbopfmkrdjwuuqyve">fatcat:yowqe4rysfbopfmkrdjwuuqyve</a> </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)<
<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>
more »
... 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.
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200710052446/https://arxiv.org/pdf/2007.00152v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext">
<button class="ui simple right pointing dropdown compact black labeled icon button serp-button">
<i class="icon ia-icon"></i>
Web Archive
[PDF]
<div class="menu fulltext-thumbnail">
<img src="https://blobs.fatcat.wiki/thumbnail/pdf/61/fe/61fe3f787370f3f8808333d230e0f9da933cac01.180px.jpg" alt="fulltext thumbnail" loading="lazy">
</div>
</button>
</a>
<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.00152v1" title="arxiv.org access">
<button class="ui compact blue labeled icon button serp-button">
<i class="file alternate outline icon"></i>
arxiv.org
</button>
</a>