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On potentially \(C_ k\)-graphic sequences. (English) Zbl 1071.05520

An \(n\)-term nonincreasing nonnegative integer sequence \(\pi = (d_1, d_2, \dots , d_n)\) is said to be graphic, if it is the degree sequence of a simple graph. Then such a graph \(G\) is called a realization of \(\pi \). In particular, let \(H\) be a graph. If a graphic sequence \(\pi \) has a realization \(G\) which contains \(H\) as its subgraph, then \(\pi \) is said to be potentially \(H\)-graphic. The paper studies potentially \(C_k\)-graphic sequences, where \(C_k\) is a circuit of length \(k\) and \(k \in \{3, 4, 5\}\).

MSC:

05C07 Vertex degrees
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