Is there a bipartite graph with the following degrees: 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 6, 6? I've tried so many different combinations and I don't think there is a way to make a bipartite graph this way, but does anyone know how I can prove this?
2026-04-24 19:39:14.1777059554
Bipartite Graph
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First hint: In a bipartite graph, the sum of the degrees on one side is equal to the sum of the degrees on the other side (each sum being equal to the number of edges). Can you split those numbers into two groups with equal sums?
Second hint: Just one of the numbers is not divisible by $3$. That is, modulo $3$, you've got eleven $0$s and a $2$.