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A Remark on the Number of Complete and Empty Subgraphs

  • RICHARD H. SCHELP (a1) and ANDREW THOMASON (a1) (a2)
    • Published online: 01 June 1998
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 [sum ]apkp(G) attains its maximum on a complete multipartite graph. We show that the same is true for a linear combination of the form [sum ]apkp(G) +bpkp(), provided bp[ges ]0 for every p.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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