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2. Graph matching - Wikipedia

   en.wikipedia.org/wiki/Graph_matching

   The case of exact graph matching is known as the graph isomorphism problem. [1] The problem of exact matching of a graph to a part of another graph is called subgraph isomorphism problem. Inexact graph matching refers to matching problems when exact matching is impossible, e.g., when the number of vertices in the two graphs are different. In ...

3. Matching (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Matching_(graph_theory)

   A maximal matching is a matching M of a graph G that is not a subset of any other 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. The following figure shows examples of maximal matchings (red) in three graphs. A maximum matching (also known as maximum-cardinality ...

4. Priority matching - Wikipedia

   en.wikipedia.org/wiki/Priority_matching

   In graph theory, a priority matching (also called: maximum priority matching) is a matching that maximizes the number of high-priority vertices that participate in the matching. Formally, we are given a graph G = ( V , E ) , and a partition of the vertex-set V into some k subsets, V 1 , …, V k , called priority classes .

5. Matching in hypergraphs - Wikipedia

   en.wikipedia.org/wiki/Matching_in_hypergraphs

   The size of a fractional matching is the sum of fractions of all hyperedges. The fractional matching number of a hypergraph H is the largest size of a fractional matching in H. It is often denoted by ν*(H). [3] Since a matching is a special case of a fractional matching, for every hypergraph H: Matching-number(H) ≤ fractional-matching-number(H)

6. Perfect matching - Wikipedia

   en.wikipedia.org/wiki/Perfect_matching

   A perfect matching can only occur when the graph has an even number of vertices. A near-perfect matching is one in which exactly one vertex is unmatched. This can only occur when the graph has an odd number of vertices, and such a matching must be maximum. In the above figure, part (c) shows a near-perfect matching.

7. Matching polytope - Wikipedia

   en.wikipedia.org/wiki/Matching_polytope

   The fifth corner (1/2,1/2,1/2) does not represent a matching - it represents a fractional matching in which each edge is "half in, half out". Note that this is the largest fractional matching in this graph - its weight is 3/2, in contrast to the three integral matchings whose size is only 1. As another example, in the 4-cycle there are 4 edges.