Randomly orthogonal factorizations in networks. (December 2016) - Zhou, Sizhong; Xu, Lan; Xu, Yang
Abstract: Let m, r, k be three positive integers. Let G be a graph with vertex set V ( G ) and edge set E ( G ), and let f: V ( G ) → N be a function such that f ( x ) ≥ ( k + 2 ) r − 1 for any x ∈ V ( G ). Let H 1, H 2, …, Hk be k vertex disjoint mr -subgraphs of a graph G . In this paper, we prove that every ( 0, m f − ( m − 1 ) r ) -graph admits a (0, f )-factorization randomly r -orthogonal to each Hi ( i = 1, 2, …, k ).