Erdős conjecture

Erdős conjecture

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. ( [http://imu.org.il/neve-ilan/comb.html#combabs apparently solved by Ron Aharoni and Eli Berger] )
* The Erdős–Mordell inequality on distances of pedal points in triangles ( [http://mathworld.wolfram.com/Erdos-MordellTheorem.html MathWorld] )
* The Erdős–Stewart conjecture on the Diophantine equation "n"! + 1 = "p""k""a"" "p""k"+1b" ( [http://www.ams.org/mathscinet-getitem?mr=2001g:11042 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.

External links

* [http://math.ucsd.edu/~fan/ep.pdf Fan Chung, "Open problems of Paul Erdős in graph theory"]


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Erdős conjecture on arithmetic progressions — Erdős conjecture on arithmetic progressions, often incorrectly referred to as the Erdős–Turán conjecture, is a conjecture in additive combinatorics due to Paul Erdős. It states that if the sum of the reciprocals of the members of a set A of… …   Wikipedia

  • Cameron–Erdős conjecture — In combinatorial mathematics, the Cameron–Erdős conjecture is the statement that the number of sum free sets contained in {1,ldots,N} is Oleft({2^{N/2 ight).The conjecture was stated by Peter Cameron and Paul Erdős in 1988. [P.J. Cameron and P.… …   Wikipedia

  • Erdős–Faber–Lovász conjecture — In graph theory, the Erdős–Faber–Lovász conjecture (1972) is a very deep problem about the coloring of graphs, named after Paul Erdős, Vance Faber, and László Lovász. It says::The union of k copies of k cliques intersecting in at most one vertex… …   Wikipedia

  • Conjecture d'Erdős sur les progressions arithmétiques — En mathématiques, plus précisément en combinatoire additive (en), la conjecture d’Erdős sur les progressions arithmétiques peut s’énoncer de la manière suivante. Soit une suite d’entiers strictement positifs ; si la série diverge, alors …   Wikipédia en Français

  • Erdos — Paul Erdős Paul Erdős, 1992 Paul Erdős (Erdős Pál …   Wikipédia en Français

  • Erdös — Paul Erdős Paul Erdős, 1992 Paul Erdős (Erdős Pál …   Wikipédia en Français

  • Erdős–Burr conjecture — Let G be a simple graph.It follows from Ramsey s theorem that there exists a least integer r(G), the Ramsey number of G , such that any complete graph on at least r(G) vertices whose edges are coloured red or blue contains a monochromatic copy of …   Wikipedia

  • Conjecture de Erdős-Burr — Conjecture d Erdős Burr Soit G un graphe simple. Il découle du théorème de Ramsey qu il existe un entier r(G) minimal, le nombre de Ramsey de G, tel que tout graphe complet d au moins r(G) sommets dont les arêtes sont coloriées en rouge et bleu… …   Wikipédia en Français

  • ERDÖS (P.) — Paul ERDÖS 1913 1996 Mathématicien brillant et hors du commun, lauréat du prix Wolf en 1983.. Né le 26 mars 1913 à Budapest et décédé le 20 septembre 1996, à Varsovie, Paul Erdös fut un enfant prodige et, à l’âge de quatre ans, il savait déjà… …   Encyclopédie Universelle

  • Conjecture De Syracuse — En mathématiques, on appelle suite de Syracuse une suite d entiers naturels définie de la manière suivante : On part d un nombre entier plus grand que zéro ; s’il est pair, on le divise par 2 ; s’il est impair, on le multiplie par… …   Wikipédia en Français

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”