# Graham, Ronald L.

## 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

## 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

## Pebbling a cartesian product ★★★

Author(s): Graham

We let denote the pebbling number of a graph .

**Conjecture**.

## Divisibility of central binomial coefficients ★★

Author(s): Graham

**Problem (1)**Prove that there exist infinitely many positive integers such that

**Problem (2)**Prove that there exists only a finite number of positive integers such that

Keywords:

## The large sets conjecture ★★★

Author(s): Brown; Graham; Landman

**Conjecture**If is 2-large, then is large.

Keywords: 2-large sets; large sets

## Graham's conjecture on tree reconstruction ★★

Author(s): Graham

**Problem**for every graph , we let denote the line graph of . Given that is a tree, can we determine it from the integer sequence ?

Keywords: reconstruction; tree