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Suppose I have a weighted graph with equal positive weight (let it be K) on each edge. Now I want to count the number of ways to assign weights to vertices SUCH THAT if there is an edge between X and Y then max(W[X], W[Y])=K where W[X] means assigned weight to vertex X.
can someone solve it in better than O(2^n).
Anyone could help me with LCM constrainsts. Please DM
Thanks
Note that for K = 2 this problem is equivalent to finding the number of vertex covers, which is #P-hard.
Even the special case of this problem $$$K=2$$$ (equivalent to counting vertex covers) is #P-complete, because counting solutions to 2-SAT is also #P-complete, and a vertex cover can easily be represented with a 2-SAT formula.
Heh, ongoing codechef again. And this is even not exactly correct reduction. Why dont they learn?..