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On Some Combinatorial Properties of Random Intersection Graphs

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Algorithms, Probability, Networks, and Games

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9295))

Abstract

In this paper, we consider a simple, yet general family of random graph models, namely Random Intersection Graphs (RIGs), which are motivated by applications in secure sensor networks, social networks and many more. In such models there is a universe \(\mathcal{M}\) of labels and each one of n vertices selects a random subset of \(\mathcal{M}\). Two vertices are connected if and only if their corresponding subsets of labels intersect. In particular, we briefly review the state of the art and we present key results from our research on the field, that highlight and take advantage of the intricacies and special structure of random intersection graphs. Finally, we present in more detail a particular result from our research, which concerns maximum cliques in the uniform random intersection graphs model (in which every vertex selects each label independently with some probability p), namely the Single Label Clique Theorem.

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Notes

  1. 1.

    A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. Consequently, the clique number of a perfect graph is equal to its chromatic number.

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Acknowledgment

This paper is devoted to our mentor Paul Spirakis, on the occasion of his 60th birthday. It was Paul who pointed out to us the very interesting model of Random Intersection Graphs and inspired us to work, as a team, on its exploration.

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Authors and Affiliations

  1. Computer Engineering and Informatics Department, University of Patras, Patras, Greece

    Sotiris E. Nikoletseas

  2. Computer Technology Institute and Press “Diophantus”, Patras, Greece

    Sotiris E. Nikoletseas & Christoforos L. Raptopoulos

Authors
  1. Sotiris E. Nikoletseas
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  2. Christoforos L. Raptopoulos
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Correspondence to Christoforos L. Raptopoulos .

Editor information

Editors and Affiliations

  1. University of Patras, Patras, Greece

    Christos Zaroliagis

  2. Technological Educational Institute of Athens, Athens, Greece

    Grammati Pantziou

  3. University of Ioannina, Ioannina, Greece

    Spyros Kontogiannis

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Nikoletseas, S.E., Raptopoulos, C.L. (2015). On Some Combinatorial Properties of Random Intersection Graphs. In: Zaroliagis, C., Pantziou, G., Kontogiannis, S. (eds) Algorithms, Probability, Networks, and Games. Lecture Notes in Computer Science(), vol 9295. Springer, Cham. https://doi.org/10.1007/978-3-319-24024-4_21

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  • DOI: https://doi.org/10.1007/978-3-319-24024-4_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24023-7

  • Online ISBN: 978-3-319-24024-4

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