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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

6 votes
2 answers
2k views

How can I prove that these two graph coloring problems are polynomial time equivalent?

Given a graph $G(V,E)$. The standard $k$-coloring problem consists in finding a feasible coloring (no two adjacent nodes share the same color) of the nodes with $k$ colors. Let this problem be $P_1$. …
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1 vote
1 answer
201 views

Show $0-1$ Knapsack is polynomially reducible to this problem

I have already posted this question here but have not received an answer so I am cross-posting with hope to reach a larger amount of mathematicians: Let $T=\{1,\cdots,n\}$ and consider the follow …
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