Practice Case When n is Odd - 6.2.2 | 6. Question 9: Proving a Graphic Sequence | Discrete Mathematics - Vol 3
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Case When n is Odd

6.2.2 - Case When n is Odd

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a graphic sequence.

💡 Hint: Think about what degree means in a graph.

Question 2 Easy

What is the Havel-Hakimi theorem used for?

💡 Hint: Recall how we prove sequences are graphic.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the required edge chromatic number for a complete graph when n is odd?

n-1
n
n+1

💡 Hint: Recall the relationship between edge chromatic numbers and vertex count.

Question 2

True or False: The Havel-Hakimi theorem can be applied to determine graphic sequences.

True
False

💡 Hint: Consider the purpose of the theorem.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the sequence [5, 5, 4, 4, 3, 3, 2, 1], prove if it is graphic and present a construction.

💡 Hint: Follow the theorem's steps for reducing the sequence.

Challenge 2 Hard

Calculate the minimum number of colors required for a complete graph of 11 vertices and explain your reasoning.

💡 Hint: Think about how odd numbers affect coloring.

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