A simple existence criterion for (g)-factors
Discrete Mathematics
Algorithms for degree constrained graph factors of minimum deficiency
Journal of Algorithms
Discrete Mathematics
Connected [a,b]-factors in K1,n-fre e graphs containing an [a,b]-factor
Discrete Mathematics
Edge-Coloring and f-Coloring for Various Classes of Graphs
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
Graph Theory With Applications
Graph Theory With Applications
Subdigraphs with orthogonal factorizations of digraphs (II)
European Journal of Combinatorics
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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 defined on V(G) such that g(x) ≤ f(x) for each x ∈ V(G). A (g, f)-factor of G is a spanning subgraph F of G such that g(x) ≤ dF(x) ≤ f(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 paper it is proved that every bipartite (mg + m - 1, mf - m + 1)-graph has (g, f)-factorizations randomly k-orthogonal to any given subgraph with km edges if k ≤ g(x) for any x ∈ V(G) and has a (g, f)-factorization k-orthogonal to any given subgraph with km edges if k - 1 ≤ g(x) for any x ∈ V(G) and that every bipartite (mg, m f)-graph has a (g, f)-factorization orthogonal to any given m-star if 0 ≤ g(x) ≤ f(x) for any x ∈ V(G). Furthermore, it is shown that there are polynomial algorithms for finding the desired factorizations and the results in this paper are in some sense best possible.