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Colouring Non-sparse Random Intersection Graphs

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 147 Accesses

Years and Authors of Summarized Original Work

  • 2009; Nikoletseas, Raptopoulos, Spirakis

Problem Definition

A proper coloring of a graph G = (V, E) is an assignment of colors to all vertices in V in such a way that no two adjacent vertices have the same color. A k-coloring of G is a coloring that uses k colors. The minimum number of colors that can be used to properly color G is the (vertex) chromatic number of G and is denoted by χ(G).

Deciding whether a given graph admits a k-coloring for a given k ≥ 3 is well known to be NP complete. In particular, it is NP hard to compute the chromatic number [5]. The best known approximation algorithm computes a coloring of size at most within a factor \(O\left (\frac{n(\log \log n)^{2}} {(\log n)^{3}} \right )\) of the chromatic number [6]. Furthermore, for any constant ε > 0, it is NP hard to approximate the chromatic number within a factor n1−ε [14].

The intractability of the vertex coloring problem for arbitrary graphs leads researchers to the...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Computer Science Department, University of Geneva, Geneva, Switzerland

    Christoforos L. Raptopoulos

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

    Christoforos L. Raptopoulos

  3. Research Academic Computer Technology Institute, Greece and Computer Engineering and Informatics Department, University of Patras, Patras, Greece

    Christoforos L. Raptopoulos

Authors
  1. Christoforos L. Raptopoulos
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Corresponding author

Correspondence to Christoforos L. Raptopoulos .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Raptopoulos, C.L. (2016). Colouring Non-sparse Random Intersection Graphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_597

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