On the factor-thickness of regular graphs

For each r-regular graph G, define a binary sequenceθ(G) = (θ 1,θ 2,...,θ r-1) byθ k = 0 if G has ak-factor, andθ k = 1 otherwise. A binary sequenceε = (ε i |i = 1, 2,...,r − 1) is said to be realizable if there exists an r-regular graph G such thatθ(G) = ε. In this paper we characterize all binary sequences which are realizable.

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