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Independence numbers of graphs and generators of ideals

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Abstract

This article investigates the generators of certain homogeneous ideals which are associated with graphs with bounded independence numbers. These ideals first appeared in the theory oft-designs. The main theorem suggests a new approach to the Clique Problem which isNP-complete. This theorem has a more general form in commutative algebra dealing with ideals associated with unions of linear varieties. This general theorem is stated in the article; a corollary to it generalizes Turán’s theorem on the maximum graphs with a prescribed clique number.

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References

  1. R. L. Graham, S.-Y. Li andW.-C. W. Li, On the structure oft-designs,S.I.A.M. J. Alg. Disc. Meth. 1 (1980) 8–14.

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  2. W.-C. W. Li andS.-Y. R. Li, On generators of ideals associated with unions of linear varieties,Bull. London Math. Soc., to appear.

  3. P. Turán, On the theory of graphs,Coll. Math. 3 (1954) 19–30.

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Author notes

  1. Wen-Ch’ing Winnie Li

    Present address: Department of Mathematics, Pennsylvania State University, 16802, University Park, PA

Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Chicago Circle, 60680, Chicago, Illinois, USA

    Shuo-Yen Robert Li & Wen-Ch’ing Winnie Li

Authors
  1. Shuo-Yen Robert Li
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  2. Wen-Ch’ing Winnie Li
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Additional information

Research supported in part by NSF Grant MCS77-03533.

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Li, SY.R., Li, WC.W. Independence numbers of graphs and generators of ideals. Combinatorica 1, 55–61 (1981). https://doi.org/10.1007/BF02579177

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  • DOI: https://doi.org/10.1007/BF02579177

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