兩題圖論
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Give a proof or a counterexample for each statement below.
a) Every graph with connectivity 4 is 2-connected.
b) Every 3-connected graph has connectivity 3.
c) Every k-connected graph is k-edge-connected.
d) Every k-edge-connected graph is k-connected.
Let G be a connected graph with at least three vertices. From G’ from G by
adding an edge with endpoints x, y whenever dG(x, y) = 2. Prove that G’ is
2-connected.
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兩題圖論
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