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The Computer Journal Advance Access originally published online on May 12, 2006
The Computer Journal 2006 49(5):585-608; doi:10.1093/comjnl/bxl018
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© The Author 2006. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

Tiziana Calamoneri*

Department of Computer Science, University of Rome ‘La Sapienza’-Italy via Salaria 113, 00198 Roma, Italy

Email: calamo{at}di.uniroma1.it

Given any fixed non-negative integer values h and k, the L(h, k)-labelling problem consists in an assignment of non-negative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with minimum span. The L(h, k)-labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach.

Key Words: Frequency assignment • radio colouring • lambda-coloring • distance-2-colouring • D2-vertex colouring


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