ABSTRACT
A partition is a division of a group of objects into disjoint sets that we call components. For example, voters in a political primary election may be partitioned into political parties, or kosher foods may be partitioned into groups that contain meat, dairy, or neither. One could also create a partition of the vertices of a graph into connected components, such as cities that are connected with each other by waterways. The criteria for creating partitions are generally symmetric and transitive. For example, it would not make sense to create a partition of cities into components that consist of cities within 500 miles of each other, or that are reachable from each other city by a direct airline flight.
