Graphs with a Small Number of Distinct Induced Subgraphs

Noga Alon, Béla Bollobás

Research output: Contribution to journalArticlepeer-review


Let G be a graph on n vertices. We show that if the total number of isomorphism types of induced subgraphs of G is at most εn2, where ε < 10−21, then either G or its complement contain an independent set on at least (1 - 4ε)n vertices. This settles a problem of Erdõs and Hajnal.

Original languageEnglish
Pages (from-to)23-30
Number of pages8
JournalAnnals of Discrete Mathematics
Issue numberC
StatePublished - 1 Jan 1989


FundersFunder number
Bat-Sheva de Rothschild
National Science FoundationDMS 8806097
Israel Academy of Sciences and Humanities


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