A Remark on the Number of Complete and Empty Subgraphs

  • Authors:

  • Richard H. Schelp;Andrew Thomason

  • Affiliations:

  • Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA (e-mail: schelpr@msci.memphis.edu);Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA (e-mail: schelpr@msci.memphis.edu) and Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, C ...

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 1998

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Abstract

Let kp(G) denote the number of complete subgraphs of order p in the graph G. Bollobás proved that any real linear combination of the form ∑apkp(G) attains its maximum on a complete multipartite graph. We show that the same is true for a linear combination of the form ∑apkp(G) +bpkp(G¯), provided bp≥0 for every p.