20. Coloring

20. Coloring - Maggie Johnson CS103B Handout#20 Graph...

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Maggie Johnson CS103B Handout #20 Graph Coloring Key Topics: * Introduction * Coloring Algorithms * Multicolorings * Coloring of Planar Graphs _____________________________________________________________________ Introduction What is the smallest number of colors (patterns) necessary to paint the map above so that no two adjacent countries are the same color? We have not done a very good job of coloring the above map… But, like virtually every other problem in the universe, this problem reduces to a graph problem, where nodes represent countries and edges represent adjacency.
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A coloring of a graph G assigns colors to the vertices of G so that adjacent vertices are given different colors. The chromatic number of a graph G is the minimal number of colors required to color G . The chromatic number of a graph G is denoted c( G ). What is the chromatic number of a tree? What is the chromatic number of a circuit in a graph? Graph coloring is a useful model for many different types of problems. For example, in scheduling: Consider the problem of attempting to schedule courses so that the number of conflicts is minimized. For example, it is probably a poor idea to schedule CIV, freshman calculus, and freshman English for MWF at 8:00am. (It would be funny, though.) If we picture every course as a node, with courses that are likely to be taken concurrently connected by an edge, then the problem of scheduling reduces to coloring the graph. In this case, each color represents a (disjoint) time to offer a course.
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20. Coloring - Maggie Johnson CS103B Handout#20 Graph...

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