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- W4384154330 abstract "Recently Chase determined the maximum possible number of cliques of size in a graph on vertices with given maximum degree. Soon afterward, Chakraborti and Chen answered the version of this question in which we ask that the graph have edges and fixed maximum degree (without imposing any constraint on the number of vertices). In this paper we address these problems on hypergraphs. For -graphs with a number of issues arise that do not appear in the graph case. For instance, for general -graphs we can assign degrees to any -subset of the vertex set with . We establish bounds on the number of -cliques in an -graph with -degree bounded by in three contexts: has vertices; has (hyper)edges; and (generalizing the previous case) has a fixed number of -cliques for some with . When is of a special form we characterize the extremal -graphs and prove that the bounds are tight. These extremal examples are the shadows of either Steiner systems or partial Steiner systems. On the way to proving our uniqueness results, we extend results of Füredi and Griggs on uniqueness in Kruskal–Katona from the shadow case to the clique case." @default.
- W4384154330 created "2023-07-14" @default.
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- W4384154330 date "2023-07-12" @default.
- W4384154330 modified "2023-09-26" @default.
- W4384154330 title "Many Cliques in Bounded-Degree Hypergraphs" @default.
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- W4384154330 doi "https://doi.org/10.1137/22m1507565" @default.
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