On a problem of Erdös and Graham

On an anti-Ramsey problem of Burr, Erdös, Graham, and T. Sós

The Graham Conjecture Implies the Erdös-turán Conjecture

Erdös and Turán once conjectured that any set A ⊂ N with

On a Diophantine Equation Related to a Conjecture of Erdös and Graham

A particular case of a conjecture of Erdös and Graham, which concerns the number of integer points on a family of quartic curves, is investigated. An absolute bound for the number of such integer points is obtained.

A Counterexample to a Conjecture of Erdös, Graham and Spencer

It is conjectured by Erdős, Graham and Spencer that if 1 ≤ a1 ≤ a2 ≤ · · · ≤ as with ∑s i=1 1/ai < n − 1/30, then this sum can be decomposed into n parts so that all partial sums are ≤ 1. In this note we propose a counterexample which gives a negative answer to this conjecture.

Minimal Decompositions of Hypergraphs into Mutually Isomorphic Subhypergraphs