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Let $G=(S,T,E)$ be a bipartite graph, $|S|=|T|$. Then the following are equivalent: 1) there exist a perfect matching in $G$; 2) there exist non-negative weights on edges such that the sum of ...

Let $G=(V,E)$ be a finite graph and let $f$ be any positive function defined on the vertices. Put weights on the vertices $v_{i}$, way $w_{i}$ so that $\sum_{i=1}^{n}w_{i}\leq 1$. Assume that every ...

I'm curious about the general question of whether any combinatorial optimization problem with polynomial time solution can necessarily be reformulated as minimizing a submodular function. The answer ...