题目内容

There is a directed graph $G = (V;E)$ with $n$ nodes and $m$ edges. Can one determine if $G$ is strongly connected in $O(m + n)$ time?

A. Yes
B. No
C. Depending on $V$ and $E$

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A graph G is bipartite iff _____.

A. it contains no even length cycle
B. it contains no odd length cycle
C. it contains no cycle

b) There is not a minimum spanning tree of $G$ that doesn’t contain the edge $e$.

A. 正确
B. 错误

Decide whether you think the following statements are true or false.Let $G$ be an arbitrary connected, undirected graph with a distinct cost on every edge. Suppose $e$ is the cheapest edge in $G$. Then,a) There is a minimum spanning tree of $G$ that contains the edge $e$.

A. 正确
B. 错误

$f=\Omega(g)\ $ and $g=\Omega(h)$, then $f=\ $_____.

A. $O(h)$
B. $\Omega(h)$
C. $\Theta(h)$