A local density condition for triangles

P. Erdős, R. J. Faudree, C. C. Rousseau, R. H. Schelp

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Abstract

Let G be a graph on n vertices and let α and β be real numbers, 0 < α, β < 1. Further, let G satisfy the condition that each ⌊αn⌋ subset of its vertex set spans at least βn 2 edges. The following question is considered. For a fixed α what is the smallest value of β such that G contains a triangle?

Original languageEnglish
Pages (from-to)153-161
Number of pages9
JournalDiscrete Mathematics
Volume127
Issue number1-3
DOIs
Publication statusPublished - Mar 15 1994

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Erdős, P., Faudree, R. J., Rousseau, C. C., & Schelp, R. H. (1994). A local density condition for triangles. Discrete Mathematics, 127(1-3), 153-161. https://doi.org/10.1016/0012-365X(92)00474-6