Induced Turán Numbers
2017 ◽
Vol 27
(2)
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pp. 274-288
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The classical Kővári–Sós–Turán theorem states that ifGis ann-vertex graph with no copy ofKs,tas a subgraph, then the number of edges inGis at mostO(n2−1/s). We prove that if one forbidsKs,tas aninducedsubgraph, and also forbidsanyfixed graphHas a (not necessarily induced) subgraph, the same asymptotic upper bound still holds, with different constant factors. This introduces a non-trivial angle from which to generalize Turán theory to induced forbidden subgraphs, which this paper explores. Along the way, we derive a non-trivial upper bound on the number of cliques of fixed order in aKr-free graph with no induced copy ofKs,t. This result is an induced analogue of a recent theorem of Alon and Shikhelman and is of independent interest.
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2019 ◽
Vol 28
(5)
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pp. 720-732
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2015 ◽
Vol Vol. 17 no. 1
(Graph Theory)
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