Discrete Mathematics - Vol 3 | 3. Vertex and Edge Colouring by Abraham | Learn Smarter
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3. Vertex and Edge Colouring

The lecture focuses on vertex and edge colouring in graph theory, emphasizing their applications such as exam scheduling and tournament match planning. It explains the concepts of vertex chromatic number and edge chromatic number, along with greedy algorithms for colouring. The complexities and challenges associated with finding the chromatic numbers are highlighted, alongside upper and lower bounds on these values.

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Sections

  • 3

    Vertex And Edge Colouring

    This section introduces vertex and edge colouring in graph theory, along with their practical applications and challenges.

    Learning Practice

  • 3.1.1

    Vertex Colouring Motivation

    This section explores the motivation behind vertex colouring problems using practical examples such as exam scheduling.

    Learning Practice

  • 3.1.2

    Vertex Colouring Problem

    The vertex colouring problem involves assigning colors to graph vertices such that no two adjacent vertices share the same color, with real-world applications such as exam scheduling.

    Learning Practice

  • 3.1.3

    Vertex Chromatic Number

    The section introduces the vertex chromatic number, focusing on its definition, significance in graph theory, and practical applications in problems like exam scheduling.

    Learning Practice

  • 3.1.4

    Greedy Algorithm For Vertex Colouring

    This section discusses the greedy algorithm for vertex colouring, its application in scheduling exams, and the challenges related to achieving optimal colouring.

    Learning Practice

  • 3.1.5

    Example Of Non-Optimal Colouring

    This section discusses the concept of vertex colouring in graph theory, illustrating the process and significance of finding optimal and non-optimal colourings.

    Learning Practice

  • 3.1.6

    Upper Bound On Vertex Chromatic Number

    This section introduces vertex coloring, focusing on its application in scheduling and defines the vertex chromatic number and its upper bound.

    Learning Practice

  • 3.2

    Edge Colouring

    This section discusses edge colouring, its significance in real-world applications, and the concept of edge chromatic number.

    Learning Practice

  • 3.2.1

    Motivation For Edge Colouring

    This section discusses the application and theoretical significance of edge colouring in graph theory, particularly focusing on its relevance in real-world scenarios like scheduling tournaments.

    Learning Practice

  • 3.2.2

    Edge Chromatic Number

    This section explores the concept of edge chromatic numbers, detailing the significance of edge coloring in graph theory and its challenges.

    Learning Practice

  • 3.2.3

    Lower And Upper Bound On Edge Chromatic Number

    This section discusses the concepts of edge chromatic number, its lower and upper bounds, and the challenges associated with determining its value.

    Learning Practice

  • 3.3

    Conclusion

    The conclusion summarizes key insights on vertex and edge colouring, emphasizing their chromatic numbers and the associated challenges.

    Learning Practice

References

ch53.pdf

Class Notes

Memorization

What we have learnt

  • Vertex colouring ensures no...
  • The vertex chromatic number...
  • The edge chromatic number i...

Final Test

Revision Tests