1-factorization of the Desargues graph: each color class is a 1-factor.The Petersen graph can be partitioned into a 1-factor (red) and a 2-factor (blue). However, the graph is not 1-factorable.
In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning k-regular subgraph, and 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 1-factor is a perfect matching, and a 1-factorization of a k-regular graph is a proper edge coloring with k colors. A 2-factor is a collection of cycles that spans all vertices of the graph.
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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...
one edge in M. A perfect matching is also called a 1-factor; see Graphfactorization for an explanation of this term. In some literature, the term complete...
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 Graphfactorization, a decomposition of a regular graph into regular subgraphs of given degrees Many problems...
triangular matrices). Let A be a square matrix. An LU factorization refers to the factorization of A, with proper row and/or column orderings or permutations...
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...
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...
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...
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...
the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution...
algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner...
true, would have numerous implications in graph theory, including the 1-factorization conjecture. For graphs in which Δ ≥ n / 3 {\displaystyle \Delta \geq...
Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography...
biconnected cubic graphs, the prism graphs have within a constant factor of the largest possible number of 1-factorizations. A 1-factorization is a partition...
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...
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...
"GraphLab: Collaborative filtering library using matrix factorization methods". Archived from the original on 2016-12-20. Retrieved 2016-12-01. "GraphLab:...
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...
ax + by = c Integer factorization: breaking an integer into its prime factors Congruence of squares Dixon's algorithm Fermat's factorization method General...
form, called factorization is, in general, too difficult to be done by hand-written computation. However, efficient polynomial factorization algorithms...
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