Orthogonal (g,f)-factorizations in graphs
Discrete Mathematics
Orthogonal factorizations of graphs
Discrete Mathematics
Some problems on factorizations with constraints in bipartite graphs
Discrete Applied Mathematics
Graph Theory
Subgraphs with orthogonal factorizations and algorithms
European Journal of Combinatorics
Subdigraphs with orthogonal factorizations of digraphs
European Journal of Combinatorics
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Let G be a digraph with vertex set V(G) and arc set E(G) and let g=(g^-,g^+) and f=(f^-,f^+) be pairs of positive integer-valued functions defined on V(G) with f(x)=g(x)=r-12 for each x@?V(G). Let H"1,H"2,...,H"r be vertex-disjoint k-subdigraphs of G. In this paper, it is proved that every (mg+(k-1)r,mf-(k-1)r)-digraph G contains a subdigraph R such that R has a (g,f)-factorization orthogonal to every H"i(1@?i@?r), where k,m and r be three positive integers with k@?m.