Colouring proximity graphs in the plane

@article{McDiarmid1999ColouringPG,
  title={Colouring proximity graphs in the plane},
  author={Colin McDiarmid and Bruce A. Reed},
  journal={Discrete Mathematics},
  year={1999},
  volume={199},
  pages={123-137}
}
Given a set V of points in the plane and given d >O, let G( V, d) denote the graph with vertex set V and with distinct vertices adjacent whenever the Euclidean distance between them is less than d. We are interested in colouring such ‘proximity’ graphs. One application where this problem arises is in the design of cellular telephone networks, where we need to assign radio channels (colours) to transmitters (points in V) to avoid interference. We investigate the case when the set V has finite… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-8 of 8 references

A unified approach to the assignment of radio channels on a regular hexagonal grid

R. A. Leese
IEEE Trans. Vehicular Technol • 1997
View 8 Excerpts
Highly Influenced

Homogeneous distribution of frequencies in a regular hexagonal cell system

IEEE Transactions on Vehicular Technology • 1982
View 5 Excerpts
Highly Influenced

Some lower bounds for a class of frequency assignment problems

IEEE Transactions on Vehicular Technology • 1986

The cellular concept

V. H. MacDonald
Bell System Tech. J • 1979

Transversal Theory, Academic Press, New York

I L. Mirsky
1971

Packing and Covering

C. A. Rogers
1964

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