On the Turán numbers of kKr in ℓ-partite graphs

Guangming Li and Jianhua Yin

Applied Mathematics and Computation, 2022, vol. 417, issue C

Abstract: Given graphs G and H, the Turán numberex(G,H)ofHinG is the maximum number of edges in a subgraph of G that contains no H. Chen et al. determined ex(Kϱ1,ϱ2,kK2) for all 1≤k≤ϱ1≤ϱ2. De Silva et al. determined ex(Kϱ1,…,ϱr,kKr) for all r≥2 and 1≤k≤ϱ1≤⋯≤ϱr. Moreover, De Silva et al. proposed an interesting generalization of ex(Kϱ1,…,ϱr,kKr): Determine ex(Kϱ1,…,ϱℓ,kKr) for ℓ≥r. In this paper, we give a proof of ex(Kϱ1,…,ϱℓ,kK2)=(k−1)∑i=2ℓϱi for all ℓ≥2 and 1≤k≤ϱ1≤⋯≤ϱℓ. We also determine the Turán numbers ex(Kϱ1,ϱ2,ϱ3,ϱ4,kK3) for all k≥1 and ϱ4≥ϱ3≥ϱ2≥ϱ1≥4(k−1), which gives a positive solution to a problem due to De Silva et al.

Keywords: Graph; Turán number; kKr (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:417:y:2022:i:c:s0096300321008730

DOI: 10.1016/j.amc.2021.126791

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