On the maximum number of copies of H in graphs with given size and order

We study the maximum number ex(n,e,H) of copies of a graph H in graphs with a given number of vertices and edges. We show that for any fixed graph H,ex(n,e,H) is asymptotically realized by the quasi‐clique provided that the edge density is sufficiently large. We also investigate a variant of this pr...

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Bibliographic Details
Published inJournal of graph theory Vol. 96; no. 1; pp. 34 - 43
Main Authors Gerbner, Dániel, Nagy, Dániel T., Patkós, Balázs, Vizer, Máté
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.01.2021
Subjects
Apexes
bipartite graph
extremal graph theory
Graph theory
Graphs
number of subgraphs
quasi‐clique
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Summary:We study the maximum number ex(n,e,H) of copies of a graph H in graphs with a given number of vertices and edges. We show that for any fixed graph H,ex(n,e,H) is asymptotically realized by the quasi‐clique provided that the edge density is sufficiently large. We also investigate a variant of this problem, when the host graph is bipartite.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.22563