A class of constructions for turán’s (3, 4)-problem
✍ Scribed by A. V. Kostochka
- Book ID
- 110564364
- Publisher
- Springer-Verlag
- Year
- 1982
- Tongue
- English
- Weight
- 243 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0209-9683
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## Abstract We explicitly construct four infinite families of irreducible triple systems with Ramsey‐Turán density less than the Turán density. Two of our families generalize isolated examples of Sidorenko 14, and the first author and Rödl 12. Our constructions also yield two infinite families of i
We employ the probabilistic method to prove a stronger version of a result of Helm, related to a conjecture of Erdos and Turan about additive bases of the positive integers. We show that for a class of random sequences of positive integers \(A\), which satisfy \(|A \cap[1, x]| \gg \sqrt{x}\) with pr