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This thesis investigates some problems related to graph colouring or more precisely graph re colouring.
Online coloring of graph. The applet below provides a dynamic environment for coloring the nodes vertices of a graph. Suppose one is given a graph g whose vertices can be properly k coloured for some k 2. Each of the paint number x p g the minimum number of colors needed for an on line coloring of g and the dp chromatic number x d p g the minimum number of colors needed for a dp coloring of g is at least the list chromatic number of g and can be much larger. It is an assignment of labels traditionally called colors to elements of a graph subject to certain constraints.
In its simplest form it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color. In graph theory graph coloring is a special case of graph labeling. The applet provides a palette of ten colors for the user to color the nodes of a graph. On line list coloring and dp coloring are generalizations of list coloring that attracted considerable attention recently.
Intuitively it is a universal on line algorithm with reasonable performance on every member of the graph family. An on line coloring algorithm is called on line competitive against a graph family if there exists an upper bound on its performance in terms of the on line chromatic number of the graphs in the family. Graph coloring is nothing but a simple way of labelling graph components such as vertices edges and regions under some constraints. This number is called the chromatic number and.
Is it possible to transform any k colouring of g into any other by recolouring vertices of g one at a time making sure a proper. In graph coloring the name of the game is to color the vertices using the fewest number of colors the only restriction being that nodes joined by an edge cannot be colored with the same color.
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