Exact Turán numbers are determined for k disjoint s-cliques and r-cliques in r-partite s-uniform hypergraphs, and for counting s-cliques in kK_r-free r-partite graphs, under explicit size conditions.
Tur\'an number of disjoint triangles in 4-partite graphs
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abstract
Let $k\ge 2$ and $n_1\ge n_2\ge n_3\ge n_4$ be integers such that $n_4$ is sufficiently larger than $k$. We determine the maximum number of edges of a 4-partite graph with parts of sizes $n_1,\dots, n_4$ that does not contain $k$ vertex-disjoint triangles. For any $r> t\ge 3$, we give a conjecture on the maximum number of edges of an $r$-partite graph that does not contain $k$ vertex-disjoint cliques $K_t$.
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math.CO 1years
2019 1verdicts
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Tur\'{a}n Problems for Vertex-disjoint Cliques in Multi-partite Hypergraphs
Exact Turán numbers are determined for k disjoint s-cliques and r-cliques in r-partite s-uniform hypergraphs, and for counting s-cliques in kK_r-free r-partite graphs, under explicit size conditions.