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?
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics