5. Apply Greedy Algorithm on the following graph using the vertex ordering v1, …., vz to obtain a proper coloring of the graph. V2 V5 V3 V4

Suppose a pail holds 12 quarts of water, the two jars hold 7 quarts and 5 quarts, and the goal is still to split the water evenly with 6 quarts in both the pail and the larger jar. Produce a complete graph model for this puzzle, and find all solutions to the water puzzle in terms of the properties of the graph.

Part D has to be from one of the graphs listed

In a high school class, there are students of different talents (ex. music, art, debate, sports, etc.). A committee needs to be formed consisting of the maximum number of students such that the committee is diverse – no two students with the same talent are in the committee. Transform this problem to a graph theoretic problem. What are the vertices of the graph? What are the edges of the graph? What do you have to find in the graph?

The sum of the degree of vertices of a graph is always an even number. O True False

In 2011 the United States federal government decided that all businesses must pay their employees a minimum wage of $7.25 per hour.  However, state governments could decide that businesses in their states should pay their employees more than the $7.25 per hour. Below is a graph of hourly minimum wage requirements for five states.   Use the information provided in the graph to decide which of the following statements is NOT TRUE!     New York's hourly wage requirement is about the same as the federal minimum wage requirement.     The hourly wage in Ohio is more than $1 above the hourly wage in Minnesota.     Oregon has the highest hourly wage requirement at over $8.00 per hour.     The hourly wage in New York is more than double the hourly wage in Georgia.

The Kentucky Derby is a horse race which takes place once a year. The horses which enter are generally male; female horses usually compete in the Kentucky Oaks which takes place the day before. In May 1995 a female horse named Serena's Song entered in the Derby and was favored to win. For most of the race she led; however near the end she was overtaken and so did not end up winning. Sketch a possible graph showing the distance of Serena's Song and the winning horse from the starting point as a function of to time, over the entire race.