2026-09-19T06:57:45Z https://api.figshare.com/v2/oai

oai:figshare.com:article/32994233 2026-05-01T00:00:00Z portal_693 item_type_8 month_year_05_2026

Inducibility and Subgraph Density Problems in Graphs Emily Cairncross (19254259) Mathematics In this thesis, we consider problems in extremal combinatorics concerning the number of copies of a fixed graph in another larger graph. Many of these problems can be phrased in terms of inducibility, i.e. the maximum proportion of induced copies of the smaller graph F in a larger graph G. We also consider how to maximize or minimize the number of copies of F in G when G has a fixed edge-density. We address these problems in a variety of settings, including edge-colored graphs, edge-weighted graphs, oriented graphs, and ordered graphs. In some of these settings, we consider the number of (not necessarily induced) subgraphs of G that are isomorphic to F, while in others we only consider the induced subgraphs of G. 2026-05-01T00:00:00Z Text Thesis 10.25417/uic.32994233.v1 https://figshare.com/articles/thesis/Inducibility_and_Subgraph_Density_Problems_in_Graphs/32994233 In Copyright