Question
Let $G$ be a connected graph. Let $T$ be a spanning tree of $G$. Prove that $T$ contains a spanning subgraph $T^{\prime}$ such that, for each vertex $v$, the degree of $v$ in $G$ and the degree of $v$ in $T^{\prime}$ are equal modulo $2 .$
Step 1
This is because the parity of the degree of a vertex is invariant under the modulo 2 operation. Show more…
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