Erdős conjecture

From Wikipedia, the free encyclopedia

The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects.

Some of these are the following:

• The Cameron–Erdős conjecture on sum-free sets of integers, solved by Green.
• The Erdős–Burr conjecture on Ramsey numbers of graphs.
• The Erdős–Faber–Lovász conjecture on coloring unions of cliques.
• The Erdős–Graham conjecture in combinatorial number theory on monochromatic Egyptian fraction representations of unity.
• The Erdős–Gyárfás conjecture on cycles with lengths equal to a power of two in graphs with minimum degree 3.
• The Erdős–Heilbronn conjecture in combinatorial number theory on the number of sums of two sets of residues modulo a prime.
• The Erdős–Mollin–Walsh conjecture on consecutive triples of powerful numbers.
• The Erdős–Menger conjecture on disjoint paths in infinite graphs. (apparently solved by Ron Aharoni and Eli Berger)
• The Erdős–Mordell inequality on distances of pedal points in triangles (MathWorld)
• The Erdős–Stewart conjecture on the Diophantine equation n! + 1 = p_k^a p_k+1^b (solved by Luca)
• The Erdős–Straus conjecture on the Diophantine equation 4/n = 1/x + 1/y + 1/z.
• The Erdős conjecture on arithmetic progressions in sequences with divergent sums of reciprocals.
• The Erdős–Woods conjecture on numbers determined by the set of prime divisors of the following k numbers.
• The Erdős–Szekeres conjecture on the number of points needed to ensure that a point set contains a large convex polygon.
• A conjecture on quickly growing integer sequences with rational reciprocal series.

[edit] External links

• Fan Chung, "Open problems of Paul Erdős in graph theory"