Turán Number of Disjoint Triangles in 4-Partite Graphs

[摘要] Let k > 2 and n1 > n2 > n3 > n4 be integers such that n4 is sufficiently largerthan k. We determine the maximum number of edges of a 4-partite graph withparts of sizes n1, . . . , n4 that does not contain k vertex-disjoint triangles. For anyr > t > 3, we give a conjecture on the maximum number of edges of an r-partitegraph that does not contain k vertex-disjoint cliques Kt.

[学科分类] 统计和概率