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So, I know that one can apply the strong LP duality theorem to specific instances of maximum flow problems to recover some nontrivial theorems in combinatorics, such as Hall's theorem, Koenig's ...

Let $G$ be a simple graph on a finite vertex set. The clique complex $X(G)$ is the simplicial complex whose faces are complete subgraphs of $G$, and the independence complex $I(G)$ is the simplicial ...

Apologies for this very basic question in matroid theory, but I could not find anything about it online after a bit of searching. There is a well-known bijective correspondence ("cryptomorphism&...

I am looking for Sperner-type lemmas where: The colors are on the edges (1-dimensional simplices) - rather than on the vertices; The target is a fully-colored vertex (a vertex adjacent to n edges of ...

Let $C$ be a simplicial complex on a finite set $V$: that means $C$ is a collection of subsets of $V$ such that if $\sigma\in C$ and $\tau\subseteq \sigma$, then $\tau\in C$. The Alexander dual $D(C)$ ...