## Abstract

Fix a k-chromatic graph F. In this paper we consider the question to determine for which graphs H does the Turán graph T_{k−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 K_{k}-Turán-good. (ii) The path P_{3} is F-Turán-good for F with χ(F)≥4. (iii) The path P_{4} and cycle C_{4} are C_{5}-Turán-good. (iv) The cycle C_{4} is F_{2}-Turán-good where F_{2} is the graph of two triangles sharing exactly one vertex.

Original language | English |
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Article number | 103519 |

Journal | European Journal of Combinatorics |

Volume | 103 |

DOIs | |

State | Published - Jun 2022 |