Graphs with no Induced $K_{2, t}$
Keyword(s):
Consider a graph $G$ on $n$ vertices with $\alpha \binom{n}{2}$ edges which does not contain an induced $K_{2, t}$ ($t \geqslant 2$). How large must $\alpha$ be to ensure that $G$ contains, say, a large clique or some fixed subgraph $H$? We give results for two regimes: for $\alpha$ bounded away from zero and for $\alpha = o(1)$. Our results for $\alpha = o(1)$ are strongly related to the Induced Turán numbers which were recently introduced by Loh, Tait, Timmons and Zhou. For $\alpha$ bounded away from zero, our results can be seen as a generalisation of a result of Gyárfás, Hubenko and Solymosi and more recently Holmsen (whose argument inspired ours).
2000 ◽
Vol 34
(1)
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pp. 20-29
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2009 ◽
pp. 385-395
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2008 ◽
Vol 29
(4)
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pp. 1055-1063
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2015 ◽
Vol 112
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pp. 18-35
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2009 ◽
Vol 13
(2)
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pp. 197-204
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2004 ◽
pp. 908-920
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2010 ◽
Vol 47
(4)
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pp. 1124-1135
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2015 ◽
Vol 07
(04)
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pp. 1550055
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1996 ◽
Vol 58
(1)
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pp. 39-42
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