@article{f63f11c216264b83bf1483c9777802be,
title = "On the maximum number of r-cliques in graphs free of complete r-partite subgraphs",
abstract = "We estimate the maximum possible number of cliques of size r in an n-vertex graph free of a fixed complete r-partite graph Ks1,s2,…,sr. By viewing every r-clique as a hyperedge, the upper bound on the Tur{\'a}n number of the complete r-partite hypergraphs gives the upper bound O(nr−1/∏i=1r−1si). We improve this to o(nr−1/∏i=1r−1si). The main tool in our proof is the graph removal lemma. We also provide several lower bound constructions.",
keywords = "Complete graphs, Complete multi-partite graphs, Generalized Tur{\'a}n problem, Graph removal lemma",
author = "J{\'o}zsef Balogh and Suyun Jiang and Haoran Luo",
note = "Research is supported in part by NSF grants DMS-1764123 and RTG DMS-1937241, FRG DMS-2152488, the Arnold O. Beckman Research Award (UIUC Campus Research Board RB 24012).Supported by Hubei Provincial Natural Science Foundation of China (2025AFB666), National Natural Science Foundation of China (11901246), China Scholarship Council (202008420064) and Institute for Basic Science (IBS-R029-C4).Research is partially supported by Trjitzinski Fellowship.The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Suyun Jiang reports financial support was provided by National Natural Science Foundation of China. Jozsef Balogh reports financial support was provided by National Science Foundation. Suyun Jiang reports financial support was provided by China Scholarship Council. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.",
year = "2025",
month = aug,
doi = "10.1016/j.disc.2025.114508",
language = "English (US)",
volume = "348",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier B.V.",
number = "8",
}