The work in this thesis can be divided into two different parts. In the first part, we suggest an approximate edge 3-coloring polynomial time algorithm for cubic graphs. For any cubic graph with n vertices, using this coloring algorithm, we get an edge 3-coloring with at most n/3 error vertices. In the second part, we study Jim
Propp's Rotor-Router model on some non-bipartite graph. We find the difference between the number of chips at vertices after performing a walk on this graph using Propp model and the expected number of chips after a random walk. It is known that for line of integers and d-dimenional grid, this deviation is constant. However, it is also proved that for k-ary infinite trees, for some initial configuration the deviation is no longer a
constant and say it is D. We present a similar study on some non-bipartite graph constructed from k-ary infinite trees and conclude that for this graph with the same initial configuration, the deviation is almost (k²)D.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/29735 |
| Date | 10 July 2008 |
| Creators | Gajewar, Amita Surendra |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Detected Language | English |
| Type | Thesis |
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