On the chromatic number of random geometric graphs

@article{McDiarmid2011OnTC,
  title={On the chromatic number of random geometric graphs},
  author={Colin McDiarmid and Tobias Mueller},
  journal={Combinatorica},
  year={2011},
  volume={31},
  pages={423-488}
}
Given independent random points X1, . . . ,Xn ∈ R d, drawn according to some probability distribution ν on Rd, and a positive distance r > 0 we construct a random geometric graph Gn with vertex set {X1, . . . ,Xn} and an edge XiXj ∈ E(Gn) when ‖Xi −Xj‖ < r. Here ‖.‖ may be an arbitrary norm on R d and we allow any probability distribution ν with a bounded density function. We consider the chromatic number χ(Gn) of Gn and its relation to the clique number ω(Gn) as n grows. We extend results by… CONTINUE READING
Highly Cited
This paper has 30 citations. REVIEW CITATIONS
18 Citations
16 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 16 references

Random Geometric Graphs

  • M. D. Penrose
  • Oxford University Press, Oxford
  • 2003
Highly Influential
15 Excerpts

Random graphs

  • S. Janson, T. Luczak, A. Rucinski
  • Wiley-Interscience Series in Discrete Mathematics…
  • 2000
1 Excerpt

Fractional graph theory

  • E. R. Scheinerman, D. H. Ullman
  • Wiley-Interscience Series in Discrete Mathematics…
  • 1997
1 Excerpt

Iii

  • M. V. Marathe, H. Breu, H. B. Hunt
  • S. S. Ravi, and D. J. Rosenkrantz. Simple…
  • 1995
1 Excerpt

Handbook of Convex Geometry

  • P. M. Gruber, J. M. Wills
  • North-Holland, Amsterdam
  • 1993
1 Excerpt

Similar Papers

Loading similar papers…