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The smallest degree sum that yields potentially Kr,r-graphic sequences

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Abstract

We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r,n) such that every n-term graphic sequence π = (d1,d2,...,dn) with term sum σ(π) = d1 + d2 + ... + dn ≥ σ(Kr,r,n) is potentially Kr,r-graphic, where Kr,r is an r × r complete bipartite graph, i.e. π has a realization G containing Kr,r as its subgraph. In this paper, the values σ(Kr,r,n) for even r and n ≥ 4r2 - r - 6 and for odd r and n ≥ 4r2 + 3r - 8 are determined.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, 230026, Hefei, China

    Jianhua Yin & Jiongsheng Li

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  1. Jianhua Yin
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  2. Jiongsheng Li
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Correspondence to Jiongsheng Li.

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Yin, J., Li, J. The smallest degree sum that yields potentially Kr,r-graphic sequences. Sci. China Ser. A-Math. 45, 694–705 (2002). https://doi.org/10.1360/02ys9076

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  • DOI: https://doi.org/10.1360/02ys9076

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