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 |
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| 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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| Summary: | 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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| ISSN: | 0195-6698 1095-9971 |
| DOI: | 10.1016/j.ejc.2022.103519 |