New York City: Bell Telephone Laboratories, Inc. [ no date ]. -7 pages. 10 7/8 x 8 3/8 inches. Typescript carbon on thin paper printed recto only. Old paperclip upper left with some creasing/marking to the leaves.
Provided with a copy of the published offprint:
[1-blank], 148-151, [1-blank] pages. 8 7/8 x 6 7/8 inches. Publisher's printed self-wrappers. Stapled. Near Fine. Wraps. 
The Journal of Mathematics and Physics, Vol XXVIII, No 2, July 1949, first published this paper. Here offered as a typescript carbon. We have included a copy of the final paper in offprint form for comparison.
"Theorem: The lines of any network can be colored so that no two lines with a common junction have the same color using at most [ (3/2)*m ] colors, where m is the maximum number of lines touching one junction. This number of colors is necessary for some networks." (p 148)
See Shannon multigraphs in Wikipedia for one example of usage. "In the mathematical discipline of graph theory, Shannon multigraphs, named after Claude Shannon by Vizing (1965), are a special type of triangle graphs, which are used in the field of edge coloring in particular." (Wikipedia)
PROVENANCE: The personal files of Claude E. Shannon (unmarked). There were four copies of this typescript carbon in Shannon's files.
Sloane and Wyner, "Claude Elwood Shannon Collected Papers," #44
Shannon, Claude E., "Journal of Mathematics and Physics," Vol XXVIII, No 2, July 1949