MAR3 1965 UNIVERSITY OF WASHINGTON SEATTLE, WASHINGTON 98105 Department of Mathematics | | | \ \ \ . af + “yrs V6. aaa pronan asaphn ; ahh J Pru tA “ PrN is pragirhanh | badd Ld =&) , choke slim 1 pes 's 5" ) yee AN ye: oO ah of ae vr att Prrering , “@ March 1, 1965 Professor Joshua Lederberg Department of Genetics Stanford University School of Medicine Stanford Medical Center 300 Pasteur Drive Palo Alto, California Dear Professor Lederberg: Many thanks for letter of February 20, and for the interesting enclosures, I hope that the copy of my re- port has reached you by now; and, of course, you are quite welcome to quote it as a forthcoming publication, Alter- natively, you might simply list the Boeing's Scientific Document number, However, I rather doubt that it will con- tain much of direct interest to you. If you should hear of any definite information as to the smallest number of vertices of trivalent polyhedral graphs “which do not admit Hamiltonian circuits, I should appreciate your telling me, for a student of mineis working on this problem at present, and is finding it rather difficult. He does have one result which might be of interest to you, and might even be useful in connection with some of your nota- tional schemes, This is the fact that every polyhedral graph can be covered by a tree of valence three; that is to say, every polyhedral graph admits a sub-tree which includes all of the vertices of the graph, but does not include more than three edges incident to any vertex, In your letter you mentioned the name of Sussenguth, I don't know his work at all, and would be glad to have a refer- ence to it, The reference to Bouwkamp is contained in my report, However, Bouwkamp does not have any spare copies of his tables nor the facilities for making them, I secured a copy of the tables by writing to Ray C. Ellis, Jr., Raytheon Company, Research Division, Waltham 54, Massachusetts. He has a copy of the tables and was able to send me a Xerox copy of his ‘(\ qat\ Carey Mow VERY Muce . dofnL 4. Hasde 1e co IR or td fon reer plamon tegley comated), Hf Asp CEQ n=l Atrnut AA Aurmyphe , The SrcblesG rgelec SOL. Professor Joshua Lederberg -2- March 1, 1965 copy upon the payment of $20.00 (or perhaps it was $25.00, I don't remember for sure), He also has some very useful pictures of a number of the graphs and some systematic way of deciding just what geometric representation to use. At a meeting of the Society for Industrial and Applied Mathematics, in New York City next June, I shall be giving an hour lecture under the title ‘Some Unsolved Geometric Problems Arising in Science and Technology.'' I know of many such problems but am always happy to hear of more so any suggestions from you would be most welcome. Some of the problems which I will discuss are really more combina- torial than geometric in nature, although they can easily be phrased in geometric terms, In this connection you may be interested in a paper by Lekkerkerker and Boland which appeared in the journal, 'fundamenta Mathematicae’, volume 21, 1962, pages 45 to 64, This paper was directly stimu- lated by a question of Seymour Benzer arising in connection with some recombination investigations on the structure of DNA molecules, Actually there are several other publica- tions in graph theory which are also related to Benzer's question,and another of my students is trying to extend these results in certain directions, Yours cordially, Victor Klee VK: jn cc: Dr. Donald W, Grace