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A clique is a subset of the vertices of a graph such that every pair of vertices in the subset is connected by an edge.

7 votes

Prove that "Finishing the degree in three years" problem is NP-Complete

Consider an instance $(G,k)$ of the clique problem: deciding whether there is a clique of size $k$ in the graph $G$. … Now we can see there is a clique of size $k$ in $G$ if and only if it is possible to finish the degree in three years. …
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2 votes

Given a set of intervals on the real line, find a minimum set of points that "cover" all the...

Your algorithm is correct. Suppose the interval with minimum end time is $[a,b]$, we only need to prove the fact that there is an optimal solution containing the time point $b$. The algorithm's correc …
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