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MATCHING GRAPH THEORY
This document discusses different types of matchings in graphs. A matching is a set of edges without common vertices. A maximum matching contains the largest possible number of edges. A maximal matching is one where no additional edges can be added without violating the matching property. A perfect matching is where every vertex is incident to exactly one edge, making it both maximum and maximal. The document provides definitions and properties of different matchings in graphs.
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MATCHING GRAPH THEORY
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- 2. A matchingor independent edge set in a graph is a set of edges without common vertices. A vertex is said to be a matched if it is incident to an edge otherwise unmatched. A matching ‘m’ that contains largest possible number of edges is called maximum matching.
- 3. A maximalmatching is a matching M of a graph G with the property that if any edge not in M is added to M, it is no longer a matching A matching M of a graph G is maximal if every edge in G has a non-empty intersection with at least one edge in M.
- 5. It isalso known as maximum cardinality matching. It is a matching that contains the largest possible number of edges. The number of edges in the maximum matching of ‘G’ is called its matching number.
- 7. A matching(M) of graph (G) is said to be a perfect match, if every vertex of graph g (G) is incident to exactly one edge of the matching (M), i.e., deg(V) = 1 ∀V Every perfect matching of graph is also a maximum matching of graph, because there is no chance of adding one more edge in a perfect matching graph.
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