Why is it impossible to partition the edges in $K_n$ into $\lfloor \frac n6 \rfloor$ planar subgraphs for $n \ge 6$?
I'm just stuck at the beginning and can't figure out how to go about this problem.
Thanks in advance for the help!
2026-03-27 22:57:34.1774652254
Partitioning the edges of $K_n$ into $\lfloor \frac n6 \rfloor$ planar subgraphs
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Hint: Show that at least one of the $\lfloor \frac{n}{6}\rfloor$ subgraphs must contain more than $3n - 6$ edges.