Find the edge chromatic number of Kₙ when n is a positive integer.

2. Draw a parsing tree for a. (8x – y)5 – 7/4z – 3. b. (a – (3+2b))/(c² + d). - - -

Suppose we assign every element of Z x Z (think coordinate plane) one of three colors: cyan, magenta, or yellow. Show that there must exist a rectangle, with sides parallel to the axes, whose vertices are all the same color.

For which values of n does the graph Wn have an Euler circuit?

Exercise 1. Find the chromatic number x and chromatic index x for each of the graphs below. Give minimal colorings for each and explain why your answers are minimal.

Let K, be a graph obtained from K, by deleting one edge. How many subgraphs of K, are isomorphic to K, ?

6.) Give a proper coloring for the two graphs below. Then determine the chromatic number of each, Justifi your answer. √1 V3 G₁ V4 V5 VS V4 V1 Ga V3 √₂