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如果T是一个树,求证任意一对最长路径必然相交.这里最长指这个路径(path)的遍(edge)的数量最多

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如果T是一个树,求证任意一对最长路径必然相交.这里最长指这个路径(path)的遍(edge)的数量最多
如果T是一个树,求证任意一对最长路径必然相交.这里最长指这个路径(path)的遍(edge)的数量最多
Let U=u_0u_1...u_m and W=w_0w_1...w_m be two longest path in T.
Assume they do not intersect.
Since T is connected,
there exists, uniquely, a path, say, L, from u_0 to w_0.
Without loss of generality, we can suppose that
L=u_0u_1...u_s v_1v_2...v_r w_tw_{t-1}...w_0,
where 0