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Some Rainbow Problems in Graphs Have Complexity Equivalent to Satisfiability Problems

Abstract : In a vertex-coloured graph, a set of vertices S is said to be a rainbow set if every colour in the graph appears exactly once in S. We investigate the complexities of various problems dealing with domination in vertex-coloured graphs (existence of rainbow dominating sets, of rainbow locating-dominating sets, of rainbow identifying sets), including when we ask for a unique solution: we show equivalence between these complexities and those of the well-studied Boolean satisfiability problems.
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https://hal.archives-ouvertes.fr/hal-02916921
Contributor : Antoine Lobstein <>
Submitted on : Monday, November 30, 2020 - 3:00:20 PM
Last modification on : Friday, July 2, 2021 - 11:20:45 AM
Long-term archiving on: : Monday, March 1, 2021 - 7:22:28 PM

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  • HAL Id : hal-02916921, version 1

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Olivier Hudry, Antoine Lobstein. Some Rainbow Problems in Graphs Have Complexity Equivalent to Satisfiability Problems. International Transactions in Operational Research, Wiley, inPress. ⟨hal-02916921⟩

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