Some factorizations of $10\sp{n}\pm 1$

Some factorizations of graphs into C5-Factors and 1-Factors

Rigorous Perturbation Bounds of Some Matrix Factorizations

This article presents rigorous normwise perturbation bounds for the Cholesky, LU and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algorithms. The used approach is a combination of the classic and refined matrix equation approaches. Each of th...

Factorizations of some weighted spanning tree enumerators

We give factorizations for weighted spanning tree enumerators of Cartesian products of complete graphs, keeping track of fine weights related to degree sequences and edge directions. Our methods combine Kirchhoff’s Matrix-Tree Theorem with the technique of identification of factors.

Excessive near 1-factorizations

We begin the study of sets of near 1-factors of graphs G of odd order whose union contains all the edges of G and determine, for a few classes of graphs, the minimum number of near 1-factors in such sets. MSC 2000: Primary 05C70; Secondary 05C15.

1-factorizations of pseudorandom graphs

A 1-factorization of a graph G is a collection of edge-disjoint perfect matchings whose union is E(G). A trivial necessary condition for G to admit a 1-factorization is that |V (G)| is even and G is regular; the converse is easily seen to be false. In this paper, we consider the problem of finding 1-factorizations of regular, pseudorandom graphs. Specifically, we prove that an (n, d, λ)graph G ...