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Chip-firing

Subsubsection

$$n^k - \frac{n}{k}$$

Chip-firing

himwiki:Discrete Time-Cost Tradeoff Problem

Compactness of Kőnig-property

A hypergraph $$H=(V,E)$$ has the Kőnig-property if there is a set $$\mathcal{D}\subseteq E$$ of pairwise disjoint hyperedges such that there is a vertex cover consists of one vertex from each hyperedge in $$\mathcal{D}$$ . (Using this terminology Kőnig's theorem says that every finite bipartite graph has the Kőnig-property). R. Aharoni and N. Bowler formulated independently the following conjecture. If $$H=(V,E)$$ is a hypergraph such that all of its hyperedges are finite and for all finite $$E'\subseteq E$$ the hypergraph $$(V,E')$$ has the Kőnig-property, then $$H$$ has the Kőnig-property as well.

Lucchesi-Younger in infinite