計算機數學

(4分) Let $G = (V,E)$ be a simple undirected graph with $|V| = n$ and $|E| = m$. Let $G$ be a bipartite graph with partition $V = V_1 \cup V_2$. How many of the following statements are ALWAYS TRUE?

• If $G$ is connected and $m = n-1$, then $G$ is a tree.
• The number of vertices with odd degree in $G$ is even.
• If $G$ has a Hamiltonian Cycle, then $|V_1| = |V_2|$.
• If $G$ has a Hamiltonian Path, then $|V_1| = |V_2|$.