Ramsey-nice families of graphs
| 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 | 2020-07-06T14:50:10Z | |
| dc.date.available | 2020-07-06T14:50:10Z | |
| dc.date.issued | 2018-08 | |
| 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 $G$ 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. | en |
| dc.description.sponsorship | Research supported in part by a BSF grant, an ISF grant and a GIF grant. | en |
| dc.identifier.uri | https://doi.org/10.1016/j.ejc.2018.04.007 | |
| dc.identifier.uri | http://hdl.handle.net/10012/16028 | |
| 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.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |