Department of Mathematics
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. LetH1, H2, …, Hk be subgraphs of G such that |E(Hi)| = m, 1 ≤ i ≤k, and V(Hi) ∩ V(Hj) = 0 when i ≠ 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 are polynomial-time algorithms to find the desired (g, f)-factorizations.
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network, graph, (g, f)-factorization, orthogonal factorization
Lam, Peter Che Bor, Guizhen Liu, Guojun Li, and Wai Chee Shiu. "Orthogonal (g, f)-factorizations in networks." Networks 35.4 (2000): 274-278.