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Degree sequences of graphs containing a cycle with prescribed length

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Abstract

Let r ≥ 3, n ≥ r and π = (d 1, d 2, ..., d n ) be a non-increasing sequence of nonnegative integers. If π has a realization G with vertex set V (G) = {v 1, v 2, ..., v n } such that d G (v i ) = d i for i = 1, 2, ..., n and v 1 v 2 ... v r v 1 is a cycle of length r in G, then π is said to be potentially C r ″-graphic. In this paper, we give a characterization for π to be potentially C r ″-graphic.

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Authors and Affiliations

  1. Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, P.R.China

    Jian-Hua Yin

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  1. Jian-Hua Yin
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Correspondence to Jian-Hua Yin.

Additional information

This work was supported by the grant of National Natural Science Foundation of China No. 10861006 and China Scholarship Council.

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Yin, JH. Degree sequences of graphs containing a cycle with prescribed length. Czech Math J 59, 481–487 (2009). https://doi.org/10.1007/s10587-009-0032-4

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  • DOI: https://doi.org/10.1007/s10587-009-0032-4

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