The cycle property is a fundamental concept in graph theory that states that for any cycle in a graph, if the weight of an edge is greater than the weights of all other edges in that cycle, then that edge cannot be part of a minimum spanning tree (MST). This property helps in identifying which edges can be safely ignored when constructing an MST. Understanding this concept is crucial for algorithms like Prim's and Kruskal's, as it allows for efficient decision-making regarding edge selection.
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