Graph Coloring Timetable | Final Worksheet (10/10)

Question 1

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - History conflicts with Physics - History conflicts with English - History conflicts with Math - History conflicts with Chemistry - Math conflicts with Chemistry - Chemistry conflicts with Physics - Chemistry conflicts with English - Chemistry conflicts with Biology - Biology conflicts with Physics What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- History: Slot 1
- Math: Slot 2
- Chemistry: Slot 3
- Biology: Slot 1
- Physics: Slot 2
- English: Slot 2

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 2

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Physics conflicts with Math - Physics conflicts with History - Physics conflicts with Chemistry - Biology conflicts with Math - Biology conflicts with History - Biology conflicts with Chemistry - Math conflicts with English - History conflicts with Chemistry - History conflicts with English What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Physics: Slot 1
- Biology: Slot 1
- Math: Slot 2
- History: Slot 2
- English: Slot 1
- Chemistry: Slot 3

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 3

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Chemistry conflicts with Physics - Chemistry conflicts with Math - Physics conflicts with English - Physics conflicts with Biology - Math conflicts with English - Math conflicts with Biology - English conflicts with Biology - English conflicts with CS What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Chemistry: Slot 1
- Physics: Slot 2
- Math: Slot 2
- English: Slot 1
- Biology: Slot 3
- CS: Slot 2

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 4

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - English conflicts with Physics - English conflicts with Math - CS conflicts with Physics - CS conflicts with Math - CS conflicts with Chemistry - History conflicts with Chemistry - History conflicts with Physics - Chemistry conflicts with Physics What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- English: Slot 1
- CS: Slot 1
- History: Slot 1
- Chemistry: Slot 2
- Physics: Slot 3
- Math: Slot 2

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 5

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - CS conflicts with Physics - CS conflicts with English - Physics conflicts with English - Physics conflicts with History - Biology conflicts with English - Biology conflicts with History - English conflicts with History - English conflicts with Math What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- CS: Slot 1
- Physics: Slot 2
- Biology: Slot 1
- English: Slot 3
- History: Slot 4
- Math: Slot 1

3. Colors/slots used: 4

Answer: Minimum 4 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 6

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - CS conflicts with Biology - CS conflicts with Math - CS conflicts with Chemistry - Biology conflicts with Physics - Biology conflicts with History - Math conflicts with Chemistry - Chemistry conflicts with Physics - Chemistry conflicts with History What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- CS: Slot 1
- Biology: Slot 2
- Math: Slot 2
- Chemistry: Slot 3
- History: Slot 1
- Physics: Slot 1

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 7

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - English conflicts with CS - English conflicts with Chemistry - English conflicts with Biology - Biology conflicts with Math - CS conflicts with Math - History conflicts with Math - History conflicts with Chemistry What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- English: Slot 1
- Biology: Slot 2
- CS: Slot 2
- History: Slot 1
- Chemistry: Slot 2
- Math: Slot 3

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 8

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Biology conflicts with History - Biology conflicts with Physics - Biology conflicts with Chemistry - Biology conflicts with English - Math conflicts with History - History conflicts with Physics - History conflicts with English - History conflicts with Chemistry - Physics conflicts with English What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Biology: Slot 1
- Math: Slot 1
- History: Slot 2
- Physics: Slot 3
- Chemistry: Slot 3
- English: Slot 4

3. Colors/slots used: 4

Answer: Minimum 4 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 9

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - CS conflicts with Math - CS conflicts with History - CS conflicts with Chemistry - CS conflicts with English - Biology conflicts with Math - Biology conflicts with Chemistry - English conflicts with Chemistry - Math conflicts with Chemistry What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- CS: Slot 1
- Biology: Slot 1
- English: Slot 2
- Math: Slot 2
- History: Slot 2
- Chemistry: Slot 3

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 10

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - English conflicts with Biology - English conflicts with Chemistry - English conflicts with CS - English conflicts with Physics - English conflicts with Math - Physics conflicts with Chemistry - Physics conflicts with Biology - Biology conflicts with CS - Biology conflicts with Math - Chemistry conflicts with CS What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- English: Slot 1
- Physics: Slot 2
- Biology: Slot 3
- Chemistry: Slot 3
- CS: Slot 2
- Math: Slot 2

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 11

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Chemistry conflicts with English - Chemistry conflicts with Biology - Chemistry conflicts with Physics - Chemistry conflicts with History - English conflicts with Biology - English conflicts with History - English conflicts with Physics - Biology conflicts with History - Physics conflicts with Math What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Chemistry: Slot 1
- English: Slot 2
- Biology: Slot 3
- Physics: Slot 3
- History: Slot 4
- Math: Slot 1

3. Colors/slots used: 4

Answer: Minimum 4 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 12

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - History conflicts with English - History conflicts with CS - History conflicts with Physics - History conflicts with Biology - English conflicts with CS - English conflicts with Physics - English conflicts with Math - English conflicts with Biology - CS conflicts with Math - Physics conflicts with Math What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- History: Slot 1
- English: Slot 2
- CS: Slot 3
- Physics: Slot 3
- Math: Slot 1
- Biology: Slot 3

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 13

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - English conflicts with CS - English conflicts with Physics - English conflicts with History - Biology conflicts with History - Biology conflicts with Physics - Biology conflicts with Math - Biology conflicts with CS - History conflicts with CS - History conflicts with Physics - CS conflicts with Physics What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- English: Slot 1
- Biology: Slot 1
- History: Slot 2
- CS: Slot 3
- Physics: Slot 4
- Math: Slot 2

3. Colors/slots used: 4

Answer: Minimum 4 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 14

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - CS conflicts with History - CS conflicts with English - CS conflicts with Chemistry - Physics conflicts with Biology - Physics conflicts with History - Physics conflicts with Chemistry - History conflicts with English - Biology conflicts with Chemistry What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- CS: Slot 1
- Physics: Slot 1
- History: Slot 2
- Biology: Slot 2
- English: Slot 3
- Chemistry: Slot 3

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 15

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - History conflicts with CS - History conflicts with English - History conflicts with Physics - History conflicts with Chemistry - Chemistry conflicts with CS - Chemistry conflicts with Math - Chemistry conflicts with Physics - CS conflicts with English - English conflicts with Physics What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- History: Slot 1
- Chemistry: Slot 2
- CS: Slot 3
- English: Slot 2
- Math: Slot 1
- Physics: Slot 3

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 16

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Chemistry conflicts with Biology - Chemistry conflicts with Math - Chemistry conflicts with English - Chemistry conflicts with History - CS conflicts with Biology - CS conflicts with English - History conflicts with Math - History conflicts with English - Biology conflicts with English What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Chemistry: Slot 1
- CS: Slot 1
- History: Slot 2
- Biology: Slot 2
- Math: Slot 3
- English: Slot 4

3. Colors/slots used: 4

Answer: Minimum 4 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 17

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - History conflicts with CS - History conflicts with Physics - History conflicts with Math - English conflicts with Chemistry - English conflicts with CS - English conflicts with Math - English conflicts with Physics - Chemistry conflicts with Math - Physics conflicts with CS - Physics conflicts with Math What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- History: Slot 1
- English: Slot 1
- Chemistry: Slot 2
- Physics: Slot 2
- CS: Slot 3
- Math: Slot 3

3. Colors/slots used: 3

Answer: Minimum 3 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 18

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Math conflicts with Biology - Math conflicts with Physics - Math conflicts with History - Chemistry conflicts with English - English conflicts with Physics - English conflicts with History - English conflicts with Biology - Biology conflicts with Physics - Biology conflicts with History What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Math: Slot 1
- Chemistry: Slot 1
- English: Slot 2
- Biology: Slot 3
- Physics: Slot 4
- History: Slot 4

3. Colors/slots used: 4

Answer: Minimum 4 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 19

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Biology conflicts with English - Biology conflicts with Physics - Biology conflicts with History - Biology conflicts with Math - Math conflicts with English - Math conflicts with Physics - Math conflicts with History - English conflicts with Physics - English conflicts with CS - English conflicts with History - CS conflicts with Physics What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Biology: Slot 1
- Math: Slot 2
- English: Slot 3
- CS: Slot 1
- Physics: Slot 4
- History: Slot 5

3. Colors/slots used: 5

Answer: Minimum 5 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Question 20

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Chemistry conflicts with CS - Chemistry conflicts with Physics - History conflicts with Biology - History conflicts with English - History conflicts with CS - History conflicts with Physics - CS conflicts with Physics - Biology conflicts with English What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Chemistry: Slot 1
- History: Slot 1
- CS: Slot 2
- Biology: Slot 2
- Physics: Slot 3
- English: Slot 4

3. Colors/slots used: 4

Answer: Minimum 4 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

Graph Coloring Timetable: Worksheet 10 - Expert Practice Graph Coloring Timetable EXPERT

What you'll learn in this worksheet: