Abstract
The L(p, q)-Edge-Labelling problem is the edge variant of the well-known L(p, q)-Labelling problem. It is equivalent to the L(p, q)-Labelling problem itself if we restrict the input of the latter problem to line graphs. So far, the complexity of L(p, q)-Edge-Labelling was only partially classified in the literature. We complete this study for all \(p,q\ge 0\) by showing that whenever \((p,q)\ne (0,0)\), the L(p, q)-Edge-Labelling problem is NP-complete. We do this by proving that for all \(p,q\ge 0\) except \(p=q=0\), there is an integer k so that L(p, q)-Edge-k-Labelling is NP-complete.
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Notes
- 1.
See http://wwwusers.di.uniroma1.it/~calamo/survey.html for later results.
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Berthe, G., Martin, B., Paulusma, D., Smith, S. (2022). The Complexity of L(p, q)-Edge-Labelling. In: Mutzel, P., Rahman, M.S., Slamin (eds) WALCOM: Algorithms and Computation. WALCOM 2022. Lecture Notes in Computer Science(), vol 13174. Springer, Cham. https://doi.org/10.1007/978-3-030-96731-4_15
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