[seqfan] Re: Is 52 prime-partitionable?

[M. F. Hasler]

On Sun, Jun 29, 2014 at 11:06 AM, Richard J. Mathar
<mathar at mpia-hd.mpg.de> wrote:
> There is a definition of prime-partitionable numbers n as follows:
> An integer n>=2 is said to be prime-partitionable if there is a
> partition {P1,P2} of the set P of all primes less than n such that, for
> all natural numbers n1 and n2 satisfying n1+n2=n we have that either
> gcd(n1,p1) <> 1 or gcd(n2,p2) <> 1 or both, for some pair (p1,p2) = P1 X P2.
>
> Taken from:
> W. Holsztynski, R. F. E. Strube, Paths and circuits in finite groups, Discr. Math. 22 (1987) 263-272, doi

NB: this is Volume 22, Issue 3, 1978 (not 1987 !)
doi:10.1016/0012-365X(78)90059-6

> and apparently the same as in
> W. T. Trotter, Jr, When the Cartesian product of directed cycles is Hamiltonian, J. Graph Theory 2 (1978) 137-142

=> DOI: 10.1002/jgt.3190020206

but the definition in Trotter-Erdös is considerably different, cf.p.141 in
http://people.math.gatech.edu/~trotter/papers/21.pdf

Maximilian.