Document Zbl 1522.05220

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J. Comb.</a> <a href="/?q=in%3A502510" title="Articles in this Issue">114, Article ID 103793, 19 p. (2023)</a>. </div> <div class="abstract">Summary: The generalized Turán number $\operatorname{ex}(n,K_s , H )$ is the maximum number of complete graph $K_s$ in an $H$-free graph on $n$ vertices. Let $F_k$ be the friendship graph consisting of $k$ triangles. Erdős and Sós (see <span class="zbmathjax-textit">V. T. Sós</span> [in: Colloquio internazionale sulle teorie combinatorie con la collaborazione della American Mathematical Society, Roma, 3–15 settembre 1973. Tomo II. Roma: Accademia Nazionale dei Lincei. 223–233 (1976; <a href="/0361.05022">Zbl 0361.05022</a>)]) determined the value of $\operatorname{ex}(n,K_3 , F_2 )$. <span class="zbmathjax-textit">N. Alon</span> and <span class="zbmathjax-textit">C. Shikhelman</span> [J. Comb. Theory, Ser. B 121, 146–172 (2016; <a href="/1348.05100">Zbl 1348.05100</a>)] proved that $\operatorname{ex}(n,K_3 , F_k ) \leq ( 9 k - 15 ) ( k + 1 ) n$. In this paper, by using a method developed by <span class="zbmathjax-textit">F. R. K. Chung</span> and <span class="zbmathjax-textit">P. Frankl</span> [Graphs Comb. 3, 111–126 (1987; <a href="/0633.05051">Zbl 0633.05051</a>)] in hypergraph theory, we determine the exact value of $\operatorname{ex}(n,K_3 , F_k )$ and the extremal graph for any $F_k$ when $n \geq 4 k^3$.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7745025">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7745025">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C30" title="MSC2020">05C30</a> </td> <td class="space"> Enumeration in graph theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C65" title="MSC2020">05C65</a> </td> <td class="space"> Hypergraphs </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ageneralized+Tur%C3%A1n+number">generalized Turán number</a>; <a href="/?q=ut%3A%5C%28H%5C%29-free+graph">$H$-free graph</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0361.05022">Zbl 0361.05022</a>; <a href="/1348.05100">Zbl 1348.05100</a>; <a href="/0633.05051">Zbl 0633.05051</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1522.05220" data-ciurl="/ci/07745025" data-biburl="/bibtex/07745025.bib" data-amsurl="/amsrefs/07745025.bib" data-xmlurl="/xml/07745025.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07745025.pdf" title="Zbl 1522.05220 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.ejc.2023.103793" aria-label="DOI for “The maximum number of triangles in $F_k$-free graphs”" title="10.1016/j.ejc.2023.103793">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2207.10162"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by-nc-nd/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nc.svg" alt="Creative Commons NC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nd.svg" alt="Creative Commons ND license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Alon, N.; Shikhelman, C., Many $T$ copies in $H$-free graphs, J. 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