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A graph that can be represented in the plane with non-crossing edges is called planar (e.g., trees, rings, square grids, etc). Give a distributed algorithm to 6-color a planar graph.1 Assume the graph has n nodes and m edges. Your proof should be based on the following steps. 1.] Assume Euler's Inequality2 which states that if n2 3 then ms 3n - 6. Use this and the handshake theorem to show that in any planar graph there is always a vertex of degree at most 5. 2. Use Part 1 above to give distributed coloring algorithm. Hint: Make use of the vertices of degree at most 5.

A graph that can be represented in the plane with non-crossing edges is called planar (e.g., trees, rings, square grids, etc). Give a distributed algorithm to 6-color a planar graph.1 Assume the graph has n nodes and m edges. Your proof should be based on the following steps. 1.] Assume Euler's Inequality2 which states that if n2 3 then ms 3n - 6. Use this and the handshake theorem to show that in any planar graph there is always a vertex of degree at most 5. 2. Use Part 1 above to give distributed coloring algorithm. Hint: Make use of the vertices of degree at most 5.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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A graph that can be represented in the plane with non-crossing edges is called planar (e.g., trees, rings, square grids, etc). Give a distributed algorithm to 6-color a planar graph.1 Assume the graph has n nodes and m edges. Your proof should be based on the following steps. 1.] Assume Euler's Inequality2 which states that if n2 3 then ms 3n - 6. Use this and the handshake theorem to show that in any planar graph there is always a vertex of degree at most 5. 2. Use Part 1 above to give distributed coloring algorithm. Hint: Make use of the vertices of degree at most 5. Prove its correctness.
Transcribed Image Text:A graph that can be represented in the plane with non-crossing edges is called planar (e.g., trees, rings, square grids, etc). Give a distributed algorithm to 6-color a planar graph.1 Assume the graph has n nodes and m edges. Your proof should be based on the following steps. 1.] Assume Euler's Inequality2 which states that if n2 3 then ms 3n - 6. Use this and the handshake theorem to show that in any planar graph there is always a vertex of degree at most 5. 2. Use Part 1 above to give distributed coloring algorithm. Hint: Make use of the vertices of degree at most 5. Prove its correctness.
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