Practice Question 10: Edge Colouring In Graphs (6.1) - Question 9: Proving a Graphic Sequence

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is edge colouring?
Show hintHide hint
Think about how edges interact in a graph.
Question 2.
How many edges can you colour with one colour if n is even?
Show hintHide hint
Consider the relationship between vertices and edges.
3Question 3.
What is the maximum number of edges that can be coloured with the same colour in an even vertex graph?
- n
- n/2 + 1
- n - 1
Show hintHide hint
Remember how the count of edges relates to vertices.
4Question 4.
Is it possible to colour an odd vertex graph with fewer than n colours?
- True
- False
Show hintHide hint
Consider how edges would conflict.
Question 5.
Given a complete graph with 9 vertices, calculate the minimum number of colours needed for a proper edge colouring and justify your reasoning.
Show hintHide hint
Visualize how edges conflict with one another.
Question 6.
Create a colour assignment for a complete graph with 6 vertices, ensuring all edges are coloured distinctly. Provide a visual representation.
Show hintHide hint
Draw it out to see the conflicts.

4 more questions in this section. Enroll free to practise them all.