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Graph Coloring Timetable

Graph Coloring Timetable problems involve scheduling courses or events that have conflicts (cannot be at same time). Each conflict is an edge in a graph, and the minimum number of time slots equals the chromatic number of the conflict graph.

10Worksheets
200+Practice Questions
AdvancedDifficulty
3-4 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Graph Coloring Timetable

Graph Coloring Timetable problems involve scheduling courses or events that have conflicts (cannot be at same time). Each conflict is an edge in a graph, and the minimum number of time slots equals the chromatic number of the conflict graph.

Prerequisites

Graph coloring concept Chromatic number Conflict detection Greedy coloring algorithm
Why This Matters: Graph Coloring problems appear in 1-2 questions in advanced exams like CAT. They test graph theory and constraint satisfaction.

How to Solve Graph Coloring Timetable Problems

1

Step 1: Create vertices for each course/event

2

Step 2: Draw edges between courses that cannot be at same time (conflicts)

3

Step 3: Apply greedy coloring algorithm: assign smallest available color to each vertex

4

Step 4: Number of colors used = minimum time slots needed

5

Step 5: Answer with number of time slots

Pro Strategy: The chromatic number (minimum colors) is the answer. For small graphs, try to find a coloring with few colors. Triangle = 3 colors.

Example Problem

Example: Courses: Math, Physics, Chemistry, Biology, English. Conflicts: Math-Physics, Math-Chemistry, Physics-Chemistry, Biology-English. Minimum time slots? Solution: Step 1: Graph with 5 vertices Step 2: Edges: M-P, M-C, P-C, B-E Step 3: M,P,C form triangle → need 3 colors Step 4: B and E are connected → need 2 colors, but can reuse colors from first set Step 5: Total colors needed = 3 Answer: 3 time slots

Pro Tips & Tricks

  • Clique (complete subgraph) of size k requires at least k colors
  • Triangle (K₃) needs 3 colors
  • Bipartite graph needs 2 colors
  • Greedy coloring works well for small graphs
  • Color classes represent same-time slots
  • No two adjacent vertices share same color

Shortcut Methods to Solve Faster

Largest clique size = lower bound for chromatic number
If graph is bipartite, χ = 2
If graph is complete, χ = n
For cycle Cₙ: χ = 2 if n even, 3 if n odd

Common Mistakes to Avoid

Assuming conflicts are transitive (not necessarily)
Using number of edges to determine colors (clique size matters more)
Forgetting that non-conflicting courses can share time slots
Not checking if fewer colors are possible

Exam Importance

Graph Coloring Timetable is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
0-1 questions
BANKING PO
1-2 questions
RAILWAYS RRB
0-1 questions
CAT
2-3 questions
INSURANCE
0-1 questions

Ready to Master Graph Coloring Timetable?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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