Number Theory » Additive N.T.

Goldbach conjecture ★★★★

Author(s): Goldbach

Conjecture   Every even integer greater than 2 is the sum of two primes.

Keywords: additive basis; prime

Posted by Benschop
updated June 14th, 2013
3 comments
Group Theory

Growth of finitely presented groups ★★★

Author(s): Adyan

Problem   Does there exist a finitely presented group of intermediate growth?

Keywords: finitely presented; growth

Posted by mdevos
updated November 12th, 2007
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Graph Theory » Basic G.T. » Cycles

Chords of longest cycles ★★★

Author(s): Thomassen

Conjecture   If $ G $ is a 3-connected graph, every longest cycle in $ G $ has a chord.

Keywords: chord; connectivity; cycle

Posted by mdevos
updated October 14th, 2023
1 comment
Combinatorics » Optimization

Ding's tau_r vs. tau conjecture ★★★

Author(s): Ding

Conjecture   Let $ r \ge 2 $ be an integer and let $ H $ be a minor minimal clutter with $ \frac{1}{r}\tau_r(H) < \tau(H) $. Then either $ H $ has a $ J_k $ minor for some $ k \ge 2 $ or $ H $ has Lehman's property.

Keywords: clutter; covering; MFMC property; packing

Posted by mdevos
updated November 11th, 2007
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