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A Havel-Hakimi type procedure and a sufficient condition for a sequence to be potentially S r,s -graphic

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Abstract

The split graph K r + \(\overline {{K_s}} \) on r+s vertices is denoted by S r,s . A non-increasing sequence π = (d 1, d 2, …, d n ) of nonnegative integers is said to be potentially S r,s -graphic if there exists a realization of π containing S r,s as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for π to be potentially S r,s -graphic. They are extensions of two theorems due to A.R.Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes Series 4 (1979), 251–267 and An Erdős-Gallai type result on the clique number of a realization of a degree sequence, unpublished).

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References

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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 National Natural Science Foundation of China (Grant No. 11161016) and SRF for ROCS, SEM.

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Yin, JH. A Havel-Hakimi type procedure and a sufficient condition for a sequence to be potentially S r,s -graphic. Czech Math J 62, 863–867 (2012). https://doi.org/10.1007/s10587-012-0051-4

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  • DOI: https://doi.org/10.1007/s10587-012-0051-4

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