Some exact results for generalized Turán problems
Fix a k-chromatic graph F. In this paper we consider the question to determine for which graphs H does the Turán graph Tk−1(n) have the maximum number of copies of H among all n-vertex F-free graphs (for n large enough). We say that such a graph H is F-Turán-good. In addition to some general results...
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| Published in | European journal of combinatorics Vol. 103; p. 103519 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.06.2022
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| Online Access | Get full text |
| ISSN | 0195-6698 1095-9971 |
| DOI | 10.1016/j.ejc.2022.103519 |
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| Abstract | Fix a k-chromatic graph F. In this paper we consider the question to determine for which graphs H does the Turán graph Tk−1(n) have the maximum number of copies of H among all n-vertex F-free graphs (for n large enough). We say that such a graph H is F-Turán-good. In addition to some general results, we give (among others) the following concrete results:
(i) For every complete multipartite graph H, there is k large enough such that H is Kk-Turán-good.
(ii) The path P3 is F-Turán-good for F with χ(F)≥4.
(iii) The path P4 and cycle C4 are C5-Turán-good.
(iv) The cycle C4 is F2-Turán-good where F2 is the graph of two triangles sharing exactly one vertex. |
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| AbstractList | Fix a k-chromatic graph F. In this paper we consider the question to determine for which graphs H does the Turán graph Tk−1(n) have the maximum number of copies of H among all n-vertex F-free graphs (for n large enough). We say that such a graph H is F-Turán-good. In addition to some general results, we give (among others) the following concrete results:
(i) For every complete multipartite graph H, there is k large enough such that H is Kk-Turán-good.
(ii) The path P3 is F-Turán-good for F with χ(F)≥4.
(iii) The path P4 and cycle C4 are C5-Turán-good.
(iv) The cycle C4 is F2-Turán-good where F2 is the graph of two triangles sharing exactly one vertex. |
| ArticleNumber | 103519 |
| Author | Palmer, Cory Gerbner, Dániel |
| Author_xml | – sequence: 1 givenname: Dániel surname: Gerbner fullname: Gerbner, Dániel email: gerbner@renyi.hu organization: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Hungary – sequence: 2 givenname: Cory surname: Palmer fullname: Palmer, Cory email: cory.palmer@umontana.edu organization: Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA |
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| Cites_doi | 10.1002/jgt.22390 10.1017/S0963548311000629 10.1016/0095-8956(75)90084-2 10.1016/j.jcta.2012.12.008 10.1016/j.disc.2007.08.016 10.1090/S0002-9904-1946-08715-7 10.1006/jctb.1995.1026 10.1007/BF02122689 10.1016/j.jctb.2020.05.005 10.1016/j.ejc.2019.103026 10.1016/j.jctb.2012.04.001 10.1017/S0963548309009687 10.1093/imrn/rny108 10.1016/j.disc.2019.06.022 10.1016/j.jctb.2016.03.004 10.1007/BF01789461 10.1016/j.ejc.2019.103001 |
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