Generalized Tur\'an problems for $K_{2,t}$

Abstract: We study the generalized Tur'an function

e x (n, H, F)

, when

H

or

F

is

K_{2, t}

. We determine the order of magnitude of

e x (n, H, K_{2, t})

when

H

is a tree, and determine its asymptotics for a large class of trees. We also determine the asymptotics of

e x (n, K_{2, t}, H)

in most cases.

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