#OK to post homework
#George Spahn, 4/4/2021, Assignment 19

# 2 I'm not immediately convinced that picking a better edge will make 
# a difference on the runtime. It seems like the contraction recursive call
# will resolve faster than the deletion recursive call, and picking a smarter
# edge does not speed up the deletion recursive tree.

# 3

# Here is a representation of the Petersen graph.
# [{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 
# {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {1, 5}, {1, 6},  {2, 7}, {3, 8}, 
# {4, 9}, {5, 10}, {6, 8}, {6, 9}, {7, 9}, {7, 10}, {8, 10}}]

# The chromatic polynomial is 
# t*(t - 1)*(t - 2)*(t^7 - 12*t^6 + 67*t^5 - 230*t^4 + 529*t^3 - 814*t^2 + 775*t - 352)
# which makes sense because the chromatic number is 3.