
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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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.](https://content.bartleby.com/qna-images/question/961032a4-1731-43fb-8f30-b8499e0ada58/c0803f14-410d-4eb4-b6ba-880f99224d57/altdfr_thumbnail.jpeg)
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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