The party problem refers to a classic problem in combinatorial mathematics and graph theory that explores the conditions under which a group of people can be divided into smaller subgroups based on specific preferences. It highlights the challenges of ensuring that within these subgroups, certain characteristics or relationships are maintained, such as friendships or rivalries. This concept has applications in various areas including social networks, voting systems, and resource allocation, showcasing the intricate balance between group dynamics and individual preferences.
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