3.1.1 - Vertex Colouring Motivation
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Practice Questions
Test your understanding with targeted questions
Define vertex colouring in the context of graph theory.
💡 Hint: Think about adjacent vertices.
What does the vertex chromatic number represent?
💡 Hint: Consider what the minimum means.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is vertex colouring?
💡 Hint: Think about where colors are assigned.
True or False: The vertex chromatic number is always equal to the number of vertices in the graph.
💡 Hint: Consider when you might need fewer colors.
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Challenge Problems
Push your limits with advanced challenges
Given a graph with 12 vertices and a maximum degree of 6, create a set of vertex color assignments that achieves optimal colouring for a scheduling scenario.
💡 Hint: Start from the highest degree vertices down.
Demonstrate a scenario in which the greedy coloring algorithm fails to produce an optimal number of colors. Construct a small graph example for clarity.
💡 Hint: Think about conflicting edges.
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