H-free subgraphs of dense graphs maximizing the number of cliques and their blow-ups

Noga Mordechai Alon, Clara Shikhelman

Research output: Contribution to journalArticle

Abstract

We consider the structure of H-free subgraphs of graphs with high minimal degree. We prove that for every k>m there exists an ϵ≔ϵ(k,m)>0 so that the following holds. For every graph H with chromatic number k from which one can delete an edge and reduce the chromatic number, and for every graph G on n>n0(H) vertices in which all degrees are at least (1−ϵ)n, any subgraph of G which is H-free and contains the maximum number of copies of the complete graph Km is (k−1)-colorable. We also consider several extensions for the case of a general forbidden graph H of a given chromatic number, and for subgraphs maximizing the number of copies of balanced blowups of complete graphs.

Original languageEnglish (US)
Pages (from-to)988-996
Number of pages9
JournalDiscrete Mathematics
Volume342
Issue number4
DOIs
StatePublished - Apr 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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