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The chromatic number of a graph is the smallest number of colors needed to color the vertices of the graph so that no two adjacent vertices share the same color. Methods used to determine this number include greedy algorithms and backtracking.

Kempe chains are used in arguments about graph coloring. They are alternating chains connecting two vertices of the same color, which allow for swapping colors along the chain to potentially reduce the number of colors used.

Edge coloring is the process of assigning colors to edges so that no two adjacent edges share the same color. The Vizing's Theorem determines the bounds on the chromatic index of a graph, which is the minimum number of colors needed.

The Welsh-Powell algorithm is a heuristic for coloring a graph. It orders the vertices in decreasing order of degree and then colors them with the lowest possible color, which is not used by its adjacent vertices.

Graph coloring is used in various applications, such as scheduling problems, register allocation in compilers, and the frequency assignment problem in wireless networks. It models scenarios where conflicts must be avoided.

The Myers-Briggs Type Indicator (MBTI) is a self-report questionnaire designed to indicate psychological preferences in how people perceive the world and make decisions. This indicator categorizes individuals into 16 distinct personality types.

Graph coloring heuristics provide approximate solutions to coloring problems. Common heuristics include greedy coloring, using largest degree ordering, or the DSATUR algorithm. These techniques aim to reduce computational complexity at the cost of potential optimality.

The Four Color Theorem states that any planar graph can be colored with no more than four colors such that no adjacent vertices have the same color. This was proven using a computer-aided proof that involved checking a large number of cases.

List coloring is a variant of graph coloring where each vertex has its own list of allowable colors, and the task is to assign a color from each vertex's list such that adjacent vertices have different colors. This is also known as the list chromatic index or choice number.