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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.
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7 Feedback arc set [2] [3]: GT8 Graph coloring [2] [3]: GT4
Matching (graph theory) – matching between different vertices of the graph; usually unrelated to preference-ordering. Envy-free matching – a relaxation of stable matching for many-to-one matching problems; Rainbow matching for edge colored graphs; Stable matching polytope; Lattice of stable matchings
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 matching [2]) is a matching that contains the largest possible number of edges. There may be many ...
In the context of the Aanderaa–Karp–Rosenberg conjecture on the query complexity of monotone graph properties, Gröger (1992) showed that any subgraph isomorphism problem has query complexity Ω(n 3/2); that is, solving the subgraph isomorphism requires an algorithm to check the presence or absence in the input of Ω(n 3/2) different edges ...
The RDF data model [1] is similar to classical conceptual modeling approaches (such as entity–relationship or class diagrams).It is based on the idea of making statements about resources (in particular web resources) in expressions of the form subject–predicate–object, known as triples.
The next example is about regular graphs. WLtest cannot distinguish regular graphs of equal order, [4]: 31 but WLpair can distinguish regular graphs of distinct degree even if they have the same order. In fact WLtest terminates after a single round as seen in these examples of order 8, which are all 3-regular except the last one which is 5-regular.
Unlike bipartite matching, the key new idea is that an odd-length cycle in the graph (blossom) is contracted to a single vertex, with the search continuing iteratively in the contracted graph. The algorithm runs in time O(| E || V | 2), where | E | is the number of edges of the graph and | V | is its number of vertices.