In graph theory, the clique-width of a graph is the minimum number of labels needed to construct by means of the following 4 operations : Creation of a new vertex v with label i (noted i) Disjoint union of two labeled graphs G and H (denoted) Joining by an edge every vertex labeled i to every vertex labeled j (denoted n) Renaming label i to label j (denoted p) Cographs are exactly the graphs with clique-width at most 2; every distance-hereditary graph has clique-width at most 3.
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SAT
The SAT is a standardized test for college admissions in the United States. The SAT is owned, published, and developed by the College Board, a nonprofit organization in the United States. It was formerly developed, published, and scored by the Educational Testing Service which still administers the exam. The test is intended to assess a student's readiness for college. It was first introduced in 1926, and its name and scoring have changed several times.
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Graph property
In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations such as particular labellings or drawings of the graph.
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Random graph
In mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs.
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Boolean satisfiability problem
In computer science, satisfiability (often written in all capitals or abbreviated SAT) is the problem of determining if the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to TRUE. Equally important is to determine whether no such assignments exist, which would imply that the function expressed by the formula is identically FALSE for all possible variable assignments.
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Chernoff bound
In probability theory, the Chernoff bound, named after Herman Chernoff, gives exponentially decreasing bounds on tail distributions of sums of independent random variables. It is better than the first or second moment based tail bounds such as Markov's inequality or Chebyshev inequality, which only yield power-law bounds on tail decay. It is related to the (historically earliest) Bernstein inequalities, and to Hoeffding's inequality. Let X1, ...
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Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
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Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size, deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria, finding "largest", "smallest", or "optimal" objects, and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems.
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