Monday, April 19, 2010

Homework #5 correction

There was a slight problem with question #2. Here is the corrected version:

2. a) Using a computer algebra system, show that the graph with edges

is 3-colorable. Use the Grobner basis you find to give an explicit 3-coloring. How many colorings are there?
b) Show that if you add edge (1,3) to the graph, it is still 3-colorable, and that the coloring is now unique up to permutation of the colors.

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