Kuratowski's Theorem is a fundamental result in graph theory that characterizes planar graphs by stating that a finite graph is planar if and only if it does not contain a subgraph that is a subdivision of the complete graph K5 or the complete bipartite graph K3,3. This theorem connects to the concept of planar graphs and has significant implications for the Four Color Theorem, which states that any planar graph can be colored using no more than four colors without adjacent vertices sharing the same color.
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