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Graph Theory
Any connected group of things can be represented as a graph: cities and roads, people and friendships, and more. Learn why an even number of people have an odd number of friends.
Excel in math and science
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Concept Quizzes
Excel in math and science
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by Brilliant Staff
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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by Brilliant Staff
Suppose a graph \(G\) is not planar. If we add an edge to \(G\) to connect two previously disconnected nodes to create the graph \(G'\), is \(G'\) planar?
Excel in math and science
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Suppose that there are three houses \(A, B, C\) and three utilities 1, 2, and 3 each of which needs to be connected by a wire to all three houses. Assuming the utilities and the houses are all points (nodes), is there a way to position them and the wires (edges) such that no two wires overlap?
Note: this is the same as asking whether \(K_{3,3}\) is a planar graph.
Excel in math and science
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It's hard to learn from lectures and videos
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Our wiki is made for math and science
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by Brilliant Staff
Suppose \(G\) is a planar graph. If we create \(G'\) by adding a single edge to \(G\), is \(G'\) planar?
Excel in math and science
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Our wiki is made for math and science
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by Brilliant Staff