On the computational complexity of the L(2,1)-labeling problem for regular graphs

Authors:
Jiří Fiala;Jan Kratochvíl
Affiliations:
Institute for Theoretical Computer Science, and Department of Applied Mathematics, Charles University, Prague;Institute for Theoretical Computer Science, and Department of Applied Mathematics, Charles University, Prague
Venue:
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Year:
2005

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Abstract

An L(2,1)-labeling of a graph of span t is an assignment of integer labels from {0,1,...,t} to its vertices such that the labels of adjacent vertices differ by at least two, while vertices at distance two are assigned distinct labels. We show that for all k ≥ 3, the decision problem whether a k-regular graph admits an L(2,1)-labeling of span k+2 is NP-complete. This answers an open problem of R. Laskar.