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

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

Some Problems on Factorizations with Constraints in Bipartite Graphs

Let G = (X; Y; E(G)) be a bipartite graph with vertex set V (G) = X ∪ Y and edge set E(G) and let g and f be two non-negative integer-valued functions de1ned on V (G) such that g(x)6f(x) for each x∈V (G). A (g; f)-factor of G is a spanning subgraph F of G such that g(x)6dF (x)6f(x) for each x∈V (F); a (g; f)-factorization of G is a partition of E(G) into edge-disjoint (g; f)-factors. In this pa...

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

Orthogonal (g, f)-Factorizations in Networks1

Let G = (V,E) be a graph and let g and f be two integer-valued functions defined on V such that k ≤ g(x) ≤ f(x) for all x ∈ V . Let H1,H2, · · · ,Hk be subgraphs of G such that |E(Hi)| = m, 1 ≤ i ≤ k, and V (Hi) ∩ V (Hj) = ∅ when i 6= j. In this paper it is proved that every (mg + m − 1,mf −m + 1)-graph G has a (g, f)-factorization orthogonal to Hi for i = 1, 2, · · · , k and shown that there a...

Orthogonal (g, f)-factorizations in networks

Let G = (V,E) be a graph and let g and f be two integer-valued functions defined on V such that k ≤ g(x) ≤ f(x) for all x ∈ V . Let H1,H2, · · · ,Hk be subgraphs of G such that |E(Hi)| = m, 1 ≤ i ≤ k, and V (Hi) ∩ V (Hj) = ∅ when i 6= j. In this paper it is proved that every (mg + m − 1,mf −m + 1)-graph G has a (g, f)-factorization orthogonal to Hi for i = 1, 2, · · · , k and shown that there a...