dc.contributor.author Aharoni, Ron dc.contributor.author Alon, Noga dc.contributor.author Amir, Michal dc.contributor.author Haxell, Penny dc.contributor.author Hefetz, Dan dc.contributor.author Jiang, Zilin dc.contributor.author Kronenberg, Gal dc.contributor.author Naor, Alon dc.date.accessioned 2020-07-06 14:50:10 (GMT) dc.date.available 2020-07-06 14:50:10 (GMT) dc.date.issued 2018-08 dc.identifier.uri https://doi.org/10.1016/j.ejc.2018.04.007 dc.identifier.uri http://hdl.handle.net/10012/16028 dc.description © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ en dc.description.abstract For a finite family $\cF$ of fixed graphs let $R_k(\cF)$ be the smallest integer $n$ for which every $k$-coloring of the edges of the complete graph $K_n$ yields a monochromatic copy of some $F\in\cF$. We say that $\cF$ is \emph{$k$-nice} if for every graph en $G$ with $\chi(G)=R_k(\cF)$ and for every $k$-coloring of $E(G)$ there exists a monochromatic copy of some $F\in\cF$. It is easy to see that if $\cF$ contains no forest, then it is not $k$-nice for any $k$. It seems plausible to conjecture that a (weak) converse holds, namely, for any finite family of graphs $\cF$ that contains at least one forest, and for all $k\geq k_0(\cF)$ (or at least for infinitely many values of $k$), $\cF$ is $k$-nice. We prove several (modest) results in support of this conjecture, showing, in particular, that it holds for each of the three families consisting of two connected graphs with $3$ edges each and observing that it holds for any family $\cF$ containing a forest with at most $2$ edges. We also study some related problems and disprove a conjecture by Aharoni, Charbit and Howard regarding the size of matchings in regular $3$-partite $3$-uniform hypergraphs. dc.description.sponsorship Research supported in part by a BSF grant, an ISF grant and a GIF grant. en dc.language.iso en en dc.publisher Elsevier en dc.rights Attribution-NonCommercial-NoDerivatives 4.0 International * dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ * dc.subject hypergraphs en dc.title Ramsey-nice families of graphs en dc.type Article en dcterms.bibliographicCitation Aharoni, Ron, Noga Alon, Michal Amir, Penny Haxell, Dan Hefetz, Zilin Jiang, Gal Kronenberg, and Alon Naor. ‘Ramsey-Nice Families of Graphs’. European Journal of Combinatorics 72 (1 August 2018): 29–44. https://doi.org/10.1016/j.ejc.2018.04.007. en uws.contributor.affiliation1 Faculty of Mathematics en uws.contributor.affiliation2 Combinatorics and Optimization en uws.typeOfResource Text en uws.peerReviewStatus Reviewed en uws.scholarLevel Faculty en
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