Maximum Common Subgraph Isomorphism Problem
In graph theory and theoretical computer science, a maximum common subgraph may mean either: * Maximum common induced subgraph, a graph that is an induced subgraph of two given graphs and has as many vertices as possible *Maximum common edge subgraph Given two graphs G and G', the maximum common edge subgraph problem is the problem of finding a graph H with as many edges as possible which is isomorphic to both a subgraph of G and a subgraph of G'. The maximum common edge subgraph problem on ...

Graph Theory
In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by ''edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ...
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Theoretical Computer Science
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's ACM SIGACT, Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of n ...
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Maximum Common Induced Subgraph
In graph theory and theoretical computer science, a maximum common induced subgraph of two graphs ''G'' and ''H'' is a graph that is an induced subgraph of both ''G'' and ''H'', and that has as many vertices as possible. Finding this graph is NP-hard. In the associated decision problem, the input is two graphs ''G'' and ''H'' and a number ''k''. The problem is to decide whether ''G'' and ''H'' have a common induced subgraph with at least ''k'' vertices. This problem is NP-complete. It is a generalization of the induced subgraph isomorphism problem, which arises when ''k'' equals the number of vertices in the smaller of ''G'' and ''H'', so that this entire graph must appear as an induced subgraph of the other graph. Based on hardness of approximation results for the maximum independent set problem, the maximum common induced subgraph problem is also hard to approximate. This implies that, unless P = NP, there is no approximation algorithm that, in polynomial time on n-vertex graphs, ...
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