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By Richard Bellman, Kenneth L. Cooke

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Extra resources for Algorithms, Graphs, and Computers, Vol. 62

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14 (1966) 255-265. E. N . Gilbert and H. 0. Pollak, “Seiner Minimal Trees,” SZAM J. Appl. Math. 16 (1968) 1-29. For an interesting account of the application of these ideas to the theory of evolution, see A . W . F. Edwards and L. L. Cavalli-Sforza, Reconstruction of Systematics Association Publication No. 6, London, 1964. 7. Evolutionary Trees, Two vertices of a graph are adjacent if they are end points of the same edge. A graph is called 2-chromatic if its vertices can be painted with 2 colors in such a way that no two adjacent vertices have the same color.

3. Suppose that the quantities a, first strictly decrease, then strictly increase as i = 1, 2, . . , n . Is there a more efficient way of finding rnin ai than by use of the step-by-step sequential procedure discussed Ili

This, in turn, allows us to treat questions of the foregoing type by quantitative means. See the Miscellaneous Exercises at the end of Chapter Eight. A few more examples from graph theory appear in the Exercises below, and many more applications will be encountered in the rest of the book. Exercises These exercises are designed to introduce the reader to additional problems and concepts of the theory of graphs. However, knowledge of these concepts will not be assumed in the rest of this book. These pages may be safely skipped in a first reading.

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