Turán number of disjoint triangles in 4-partite graphs (Q2144320)

Summary: Let \(k\geqslant 2\) and \(n_1\geqslant n_2\geqslant n_3\geqslant n_4\) 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 \(n_1, \ldots, n_4\) that does not contain \(k\) vertex-disjoint triangles. For any \(r> t\geqslant 3\), we give a conjecture on the maximum number of edges of an \(r\)-partite graph that does not contain \(k\) vertex-disjoint cliques \(K_t\).