Lecture 4 Lecturer : Mohsen
نویسنده
چکیده
In this section, we start the study of LOCAL vertex-coloring algorithms for general graphs. The eventual goal would be to obtain (∆ + 1)-coloring of the graphs — that is, an assignment of colors {1, 2, . . . ,∆ + 1} to vertices such that no two adjacent vertices receive the same color — where ∆ denotes the maximum degree. Notice that by a simple greedy argument, each graph with maximum degree at most ∆ has a (∆ + 1)-coloring: color vertices one by one, each time picking a color which is not chosen by the already-colored neighbors. However, this greedy argument does not lead to an efficient LOCAL procedure for finding such a coloring1.
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