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The Smallest Degree Sum That Yields Potentially K r+1 −K 3-Graphic Sequences

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Abstract

Let σ(K r+1 −K 3, n) be the smallest even integer such that each n-term graphic sequence π = (d 1, d 2, ··· , d n ) with term sum σ(π) = d 1 + d 2 + ··· + d n ≥ σ(K r+1 −K 3, n) has a realization containing K r+1 −K 3 as a subgraph, where K r+1 −K 3 is a graph obtained from a complete graph K r+1 by deleting three edges which form a triangle. In this paper, we determine the value σ(K r+1 −K 3, n) for r ≥ 3 and n ≥ 3r + 5.

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Authors and Affiliations

  1. School of Computer and Electronics Information, Guangxi University, Nanning, 530004, China

    Meng-xiao Yin

  2. Department of Applied Mathematics, Hainan University, Haikou, 570228, China

    Meng-xiao Yin

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  1. Meng-xiao Yin
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Correspondence to Meng-xiao Yin.

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Supported by the National Natural Science Foundation of China (No.10401010).

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Yin, Mx. The Smallest Degree Sum That Yields Potentially K r+1 −K 3-Graphic Sequences. Acta Math. Appl. Sin, Engl. Ser. 22, 451–456 (2006). https://doi.org/10.1007/s10255-006-0321-8

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  • DOI: https://doi.org/10.1007/s10255-006-0321-8

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