A bipartite graph: two-colour it, watch an odd cycle break it, split it into two sides, or build and test your own in free play.

Bipartite · two sides, crossing edges group 0 group 1 checking conflict
The two groups
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Press Play. A bipartite graph splits into two sides; we will prove it by painting every vertex the opposite colour of its neighbour.

Speed
Click two vertices to toggle an edge between them. Drag a vertex to move it. Then Test bipartite to 2-colour your graph.
vertices
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edges
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bipartite?