Frontiers of Mathematics in China >
Orthogonal factorizations of digraphs
Received date: 15 Aug 2008
Accepted date: 30 Oct 2008
Published date: 05 Jun 2009
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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) such that g-(x)≤f-(x) and g+(x)≤f+(x) for each x ∈ V (G). A (g, f)-factor of G is a spanning subdigraph H of G such that g-(x)≤idH(x)≤f-(x) and g+(x)≤odH(x)≤f+(x) for each x ∈ V (H); a (g, f)-factorization of G is a partition of E(G) into arc-disjoint (g, f)-factors. Let and H be a factorization and a subdigraph of G, respectively. is called k-orthogonal to H if each Fi, 1≤i≤m, has exactly k arcs in common with H. In this paper it is proved that every (mg+m-1,mf-m+1)-digraph has a (g, f)-factorization k-orthogonal to any given subdigraph with km arcs if k≤min{g-(x), g+(x)} for any x ∈ V (G) and that every (mg,mf)-digraph has a (g, f)-factorization orthogonal to any given directed m-star if 0≤g(x)≤f(x) for any x ∈ V (G). The results in this paper are in some sense best possible.
Key words： Digraph; (g, f)-factor; orthogonal factorization
Guizhen LIU . Orthogonal factorizations of digraphs[J]. Frontiers of Mathematics in China, 2009 , 4(2) : 311 -323 . DOI: 10.1007/s11464-009-0011-y
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