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Bounds on Quasi-Completeness

  • Malay Bhattacharyya
  • Sanghamitra Bandyopadhyay
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

Abstract

A graph G = (V,E) is γ-quasi-complete (γ ∈ [0,1]) if every vertex in G is connected to at least γ.(|V| − 1) other vertices. In this paper, we establish some relationships between the girth and the quasi-completeness of a graph. We also derive an upper bound \(\frac{1}{2}\big(1+\frac{r}{\gamma}\big) + \sqrt{\frac{1}{4}\big(1+\frac{r}{\gamma}\big)^2 + \frac{2|E|}{\gamma} - \frac{r|V|}{\gamma}}\) for the largest order γ-quasi-complete subgraph in a graph of minimum degree r.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Malay Bhattacharyya
    • 1
  • Sanghamitra Bandyopadhyay
    • 1
  1. 1.Machine Intelligence UnitIndian Statistical InstituteKolkataIndia

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