Graph Coloring via Synchronization of Coupled Oscillators

In this paper, we study the possibility of coloring graphs by means of
synchronized coupled oscillators. We consider an array of coupled
oscillators as a graph by associating the oscillators to vertices and
the coupling to edges. When the coupled array is synchronized, the
phase of the oscillators can be considered as the color associated
with the corresponding vertices. We prove that for connected
2-colorable graphs, we can construct a coupled array which generates
the 2-coloring for that graph. For the general case, numerical
simulation results with connected 3-colorable graphs suggest that the
coupled array of oscillators can color graphs with a small number of
colors in most cases. Some complexity issues of the system and
comparisons with antivoter models of graph coloring will be discussed.
We also conjecture that the system can be used to approximate the star
chromatic number of the graph.

By: Chai Wah Wu

Published in: RC20965 in 1997


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