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題解(求證明)

Posted by raincole at 2009-04-22 14:11:25 on Problem 3712

n個點,使最大匹配為k-1的最大邊數等於

(n-1) + (n-2) + ... (n-k+1)
  由一個點連到所有邊,重複做k-1次。

(2(k-1) * (2(k-1)-1) / 2) + Max(n-2(k-1), 2(k-1))
  建一個有2(k-1)個點的完全子圖S,然後由外部一個點對S全部點連線,或由S一個點
  對外部全部點連線。

這兩種構圖方式之一(我證不出來)。

如果2k>n,那麼解就是n(n-1)/2(完全圖)。

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