On the existence of a matching orthogonal to a 2-factorization
Discrete Mathematics
Graph Theory With Applications
Graph Theory With Applications
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Consider a graph G = (V, E) with an [a, b]-factorization F = {F1, F2, ..., Fm}. It is proved in this paper that: 1. there is an m-matching of G to which F is orthogonal if n = |V (G)| ≥ (2 + b/a) (m - 1) for b ≥ 2a and n ≥ 3.26m for b = a; 2. if √2b ≤ a ≤ b, then for any given edge e of G, there is a [1, a]-subgraph H of G such that e is included in H and F is orthogonal to H.