a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k-factorization. In particular...

A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to...

matching with the factorization labels in turn. Similarly add three more blocks 12CDEF, 34CDEF, and 56CDEF, replacing the factorization labels by the corresponding...

partition of the edges of the graph into factors; a k-factorization is a partition into k-factors. For instance a 1-factorization is an edge coloring with...

the corresponding graphs cannot be decomposed. In this sense, the failure of unique factorization on (possibly disconnected) graphs is akin to the statement...

decomposition into as few matchings as possible Graph factorization, a decomposition of a regular graph into regular subgraphs of given degrees Many problems...

an LDU (factorization with all diagonal entries of L and U equal to 1), then the factorization is unique. In that case, the LU factorization is also unique...

permutation matrix. A perfect matching is also called a 1-factor; see Graph factorization for an explanation of this term. In some literature, the term complete...

the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution...

\nu } . An immediate consequence of the factorization property is that morphisms in a k {\displaystyle k} -graph can be factored in multiple ways: there...

discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different...

"GraphLab: Collaborative filtering library using matrix factorization methods". Archived from the original on 2016-12-20. Retrieved 2016-12-01. "GraphLab:...

k} -regular graph with 2 n {\displaystyle 2n} vertices is 1-factorable. The perfect 1-factorization conjecture that every complete graph on an even number...

In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to...

quasi-polynomial time. The integer factorization problem is the computational problem of determining the prime factorization of a given integer. Phrased as...

Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and...

of the largest possible number of 1-factorizations. A 1-factorization is a partition of the edge set of the graph into three perfect matchings, or equivalently...

In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...

and that between them include all 5 × 3 = 15 edges of the graph; this graph factorization can be done in 6 different ways. Consider a permutation of...

polynomial time algorithm for recognizing tensor product graphs and finding a factorization of any such graph. If either G or H is bipartite, then so is their...

algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner...

hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two...

Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography...

In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From...

cubic (3-regular) graph is sometimes called a Tait coloring. Not every regular graph has a 1-factorization; for instance, the Petersen graph does not. More...

– Factorization of Mersenne numbers Mn (n up to 1280) Factorization of completely factored Mersenne numbers The Cunningham project, factorization of...

Theorem 2, p. 59, and corollary, p. 65 Tutte, W. T. (1947), "The factorization of linear graphs", The Journal of the London Mathematical Society, 22 (2): 107–111...

In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not...

Matrix factorization is a class of collaborative filtering algorithms used in recommender systems. Matrix factorization algorithms work by decomposing...

theorem) the graph is chordal (by equivalence to a Bayesian network) When such a factorization does exist, it is possible to construct a factor graph for the...