Yesterday I went to the grocery store and had to bag my own groceries. Here are some restrictions:

A dozen eggs cannot be bagged with a gallon of milk.
A loaf of bread cannot be bagged with cans of soup.
A gallon of ice cream cannot be bagged with hot rotisserie chicken.
A gallon of milk cannot be bagged with hot rotisserie chicken.
Cans of soup cannot be bagged with a dozen eggs.
A bag of spaghetti noodles cannot be bagged with cans of soup.
A dozen eggs cannot be bagged with hot rotisserie chicken.
A gallon of ice cream cannot be bagged with a loaf of bread.
A bag of spaghetti noodles cannot be bagged with a gallon of ice cream.

a. Draw a mathematical graph G with vertices and edges to represent the groceries and restrictions among them.
b. Use the greedy coloring algorithm to find one coloring assignment to each vertex.
c. what is the least number of bags for me to bring? Explain why,