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saturate (Definition)

Let $ G(V,E)$ be a graph and $ M$ a matching in $ G$. A vertex $ v\in V(G)$ is said to be saturated by $ M$ if there is an edge in $ M$ incident to $ v$. A vertex $ v\in V(G)$ with no such edge is said to be unsaturated by $ M$. We also say that $ M$ saturates $ v$.



"saturate" is owned by mathcam.
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See Also: Hall's marriage theorem, bipartite matching, matching

Other names:  saturates, saturated
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Cross-references: incident, edge, vertex, matching, graph
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This is version 1 of saturate, born on 2003-09-18.
Object id is 4735, canonical name is Saturate.
Accessed 4918 times total.

Classification:
AMS MSC: 05D15 (Combinatorics :: Extremal combinatorics :: Transversal theory)
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