Turán number of disjoint triangles in 4-partite graphs

2019/06/05 by Jie Han, Yi Zhao, Han, Jie +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1906.01812

openalex publication_date 2019/06/05 · openalex created_date 2019/06/14 · openalex updated_date 2026/07/28

Abstract

Let k≥ 2 and n₁≥ n₂≥ n₃≥ n₄ be integers such that n₄ is sufficiently larger than k. We determine the maximum number of edges of a 4-partite graph with parts of sizes n₁,…, n₄ that does not contain k vertex-disjoint triangles. For any r> t≥ 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.

Related

• Extremal numbers of disjoint triangles in r-partite graphs
• Turán number of four vertex-disjoint cliques
• Turán numbers of vertex-disjoint cliques in r-partite graphs
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• The maximum number of triangles in F_k-free graphs