Randomly orthogonal factorizations of bipartite graphs

RANDOMLY ORTHOGONAL FACTORIZATIONS OF ( 0 , mf − ( m − 1 ) r ) - GRAPHS

Let G be a graph with vertex set V (G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V (G) such that g(x) ≤ f(x) for every vertex x of V (G). We use dG(x) to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that g(x) ≤ dF (x) ≤ f(x) for every vertex x of V (F ). In particular, G is called a (g, f)-graph if G i...

Orthogonal factorizations of graphs

Let G be a graph with vertex set V (G) and edge set E (G). Let k1, k2, . . . ,km be positive integers. It is proved in this study that every [0,k1þ þ km mþ 1]-graph G has a [0, ki]1 -factorization orthogonal to any given subgraph H with m edges. 2002 Wiley Periodicals, Inc. J Graph Theory 40: 267–276, 2002

Bipartite 2-Factorizations of Complete Multipartite Graphs

It is shown that if K is any regular complete multipartite graph of even degree, and F is any bipartite 2-factor of K, then there exists a factorisation of K into F ; except that there is no factorisation of K6,6 into F when F is the union of two disjoint 6-cycles.

Randomly r-orthogonal (0, f)-factorizations of (0, mf-m+1)-graphs

Monogamous decompositions of complete bipartite graphs, symmetric H-squares, and self-orthogonal 1-factorizations

Necessary and sufficient conditions are obtained for the existence of the structures from the title of this article.