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- W3216548525 abstract "Given graphs G and H, the Turán number ex(G,H) of H in G 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." @default.
- W3216548525 created "2021-12-06" @default.
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- W3216548525 date "2022-03-01" @default.
- W3216548525 modified "2023-10-18" @default.
- W3216548525 title "On the Turán numbers of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:mrow><mml:mi>k</mml:mi><mml:msub><mml:mi>K</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow></mml:math> in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.svg><mml:mi>ℓ</mml:mi></mml:math>-partite graphs" @default.
- W3216548525 cites W2038398059 @default.
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- W3216548525 doi "https://doi.org/10.1016/j.amc.2021.126791" @default.
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