The term k5 refers to a complete graph on five vertices, denoted as K5, where every pair of distinct vertices is connected by a unique edge. In the context of planar graphs and graph coloring, K5 is significant because it serves as a classic example of a non-planar graph, meaning it cannot be drawn on a plane without edges crossing. Understanding K5 helps illustrate the limitations of planar graphs and plays a key role in concepts like graph coloring, where determining the minimum number of colors needed to color a graph's vertices without adjacent vertices sharing the same color becomes complex.
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