SLOVENSKA AKADEMIA VIED
KABINET MATEMATIKY OCT 41965

BRATISLAVA, Ulica Obrancov miera 41

| Prof. Joshua Lederberg,

Stanford University School of Medicine,
Stanford Medical Center,
Department of Genetics,

PALO ALTO,
California, USA

| _

Vaia znatka Naga znatka Vas list VY Bratislave dita September 27 1965.
, 3

Vee:
Dear Prof. Lederberg:

Thank you for your very interesting letter of June 18.
It arrived during my holiday and later I did not feel quite
well so that I could not reply immediately. I can say that
your results are in many points in close relation with ours. c

From your letter I see that we did not understand the - \
exact meaning of the formulation of your problem, We tried
to find a trivalent convex polyhedron containing exactly one

-edge /i.e., in our terminology, an edge included in no
Hamilton line; your “obligatory edges" we call & -edges;
the other edges are called S&-edges/. Now we see that you
had requested to construct a trivalent convex polyhedron
containing at_least one f8-edge. Nevertheless, this problem
was also very interesting.

Your conjecture concerning symmetries of trivalent
polyhedra is probably true but I do not know if a proof of
it has been published.

Professor Kotzig and I now are writing an article
concerning Hamilton lines and trivalent graphs for publi-
cation in Matematicko-fyzikdlny %asopis. We intend to send
you and Professor Klee copies of the manuscript as soon as
it is finished. These results will probably overlap with
yours and Professor Klee’s, but, of course, in such cases
we shall point out to this fact - if we know about it.

I am looking forward to your memorandum and any
other materials and notes concerning these questions. I
wrote also to dr. Grace /unfortunaly, I have not his paper
concerning convex polyhedra/, but I have not yet had his
reply.

AYSOG

Yours sincerely

Juraj Bos4dk