I'm having a bit of trouble with this homework problem: If $G=(V, E)$ is a connected bipartite undirected graph with $V$ partitioned as $V_1\cup V_2$, how can I prove the existence of a Hamilton path in $G$ implies that $|V_1|-|V_2|\in\{-1, 0, 1\}$?
Consequences of Hamilton Paths and Cycles
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graph-theory