SLOVENSKA AKADEMIA VIED
KABINET MATEMATIKY

BRATISLAVA, Ulica Obrancov mieru 41

Dr.Joshua Lederberg,

Professor of Genetics,

wtanford University School of Medicine,
Palo Alto, Califormia,

Ussede

Vata znatka Naga znatka Vai List

Vec:

Dear Dr. Lederberg;

Prof. Kotzig informed us in

JUN 14 1965

V Bratislave dia June Ts; 1965.

his seminary on graph theory about your

very interesting problem and he showed us your works.We can see that our inte-

rests are very close.

Ag to your problem, I discovered that polyhedra with requested

properties do exist.One of them /with 28

vertices/ is drawn on the Figure.

The red edge is contained in no of 10 Hamilton lines of the graph. What is

the connection between this problem and your research ?

The number of vertices /46/

in famous Tutte’s example can be

diminished. 5 years ago Prof. Kotzig constructed /but he did not published/

@ non-Hamilton trivalent convex polyhedron with 44 vertices.Lately I constructed

& Smilar example with 38 vertices.

i camnot understand the following sentence in your article "Hamilton

circuits of convex trivalent polyhedra";

"As Grace has noted, his criterion for

isomorphism ... is not strictly sufficient and his list may still be incomplete."

I am sending you some reprints of papers of Prof. Kotzig and one

of mine /most of them is either in knglish or with an English summary/.

we expect with interest your further results.

Yours sincerely

Vybavuje: Telefon:

an
4 “Lt
para f

a

Juraj Bosak,
Kabinet matematiky SAV,

ro -
le
sak

Palyae

ul.Obrancov mieru 41,

Bratislava, Czechoslovakia

ZT 101, 254-63