A Theorem on Coloring The Lines of a Network [offprint]
Shannon, Claude E. [Elwood]
Published by [Massachusetts Institute of Technology], [Cambridge, Massachusetts], 1949
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Kuenzig Books ( ABAA / ILAB ), Topsfield, MA, U.S.A.
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About this Item
Description:
[1-blank], 148-151, [1-blank] pages. 8 7/8 x 6 7/8 inches. Publisher's printed self-wrappers. Three separate leaves stapled twice near the spine. While oddly constructed, the reprint statement on the first leaf indicates this is an offprint and not an extract - all other examined copies from Shannon's files are identical. Wraps. The Journal of Mathematics and Physics, Vol XXVIII, No 2, July 1949, first published this paper. Here offered in offprint form with no separate wrappers (presumably as issued). "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 multiple copies of this item in Shannon's files. REFERENCES: Sloane and Wyner, "Claude Elwood Shannon Collected Papers," #44. Seller Inventory # 29797
Bibliographic Details
Title: A Theorem on Coloring The Lines of a Network...
Publisher: [Massachusetts Institute of Technology], [Cambridge, Massachusetts]
Publication Date: 1949
Binding: Wraps
Condition: Very Good