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Graham, Ronald L.


Logic

Termination of the sixth Goodstein Sequence ★

Author(s): Graham

Question   How many steps does it take the sixth Goodstein sequence to terminate?

Keywords: Goodstein Sequence

Posted by mdevos
updated September 17th, 2010
5 comments
Combinatorics

Monotone 4-term Arithmetic Progressions ★★

Author(s): Davis; Entringer; Graham; Simmons

Question   Is it true that every permutation of positive integers must contain monotone 4-term arithmetic progressions?

Keywords: monotone arithmetic progression; permutation

Posted by vjungic
updated October 3rd, 2007
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Graph Theory

Pebbling a cartesian product ★★★

Author(s): Graham

We let $ p(G) $ denote the pebbling number of a graph $ G $.

Conjecture   $ p(G_1 \Box G_2) \le p(G_1) p(G_2) $.

Keywords: pebbling; zero sum

Posted by mdevos
updated September 24th, 2007
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Number Theory » Combinatorial N.T.

Divisibility of central binomial coefficients ★★

Author(s): Graham

Problem  (1)   Prove that there exist infinitely many positive integers $ n $ such that $$\gcd({2n\choose n}, 3\cdot 5\cdot 7) = 1.$$
Problem  (2)   Prove that there exists only a finite number of positive integers $ n $ such that $$\gcd({2n\choose n}, 3\cdot 5\cdot 7\cdot 11) = 1.$$

Keywords:

Posted by maxal
updated June 29th, 2014
5 comments
Combinatorics » Ramsey Theory

The large sets conjecture ★★★

Author(s): Brown; Graham; Landman

Conjecture   If $ A $ is 2-large, then $ A $ is large.

Keywords: 2-large sets; large sets

Posted by vjungic
updated June 10th, 2007
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Graph Theory » Basic G.T.

Graham's conjecture on tree reconstruction ★★

Author(s): Graham

Problem   for every graph $ G $, we let $ L(G) $ denote the line graph of $ G $. Given that $ G $ is a tree, can we determine it from the integer sequence $ |V(G)|, |V(L(G))|, |V(L(L(G)))|, \ldots $?

Keywords: reconstruction; tree

Posted by mdevos
updated January 16th, 2013
5 comments
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