Geodesic
Generalized Turán problems for \(K_{2,t}\)
Dániel Gerbner1
1Alfred Renyi Institute of Mathematics
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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The generalized Turán function $\mathrm{ex}(n,H,F)$ denotes the largest number of copies of $H$ among $F$-free $n$-vertex graphs. We study $\mathrm{ex}(n,H,F)$ when $H$ or $F$ is $K_{2,t}$. We determine the order of magnitude of $\mathrm{ex}(n,H,K_{2,t})$ when $H$ is a tree, and determine its asymptotics for a large class of trees. We also determine the asymptotics of $\mathrm{ex}(n,K_{2,t},F)$ when $F$ has chromatic number at least three and when $F$ is bipartite with one part of order at most two.
DOI : 10.37236/10588
Classification : 05C30, 05C35
Mots-clés : Turán number, \(t\)-Füredi-good graph

Dániel Gerbner  1

1 Alfred Renyi Institute of Mathematics 
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     author = {D\'aniel Gerbner},
     title = {Generalized {Tur\'an} problems for {\(K_{2,t}\)}},
     journal = {The electronic journal of combinatorics},
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     doi = {10.37236/10588},
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Dániel Gerbner. Generalized Turán problems for \(K_{2,t}\). The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/10588

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