The external constraint 4 nonempty part sandwich problem

  • Authors:

  • Rafael B. Teixeira;Simone Dantas;Celina M. H. de Figueiredo

  • Affiliations:

  • Instituto de Ciências Exatas, Universidade Federal Rural do Rio de Janeiro, Brazil;Instituto de Matemática, Universidade Federal Fluminense, Brazil;COPPE, Universidade Federal do Rio de Janeiro, Brazil

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2011

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Abstract

List partitions generalize list colourings. Sandwich problems generalize recognition problems. The polynomial dichotomy (NP-complete versus polynomial) of list partition problems is solved for 4-dimensional partitions with the exception of one problem (the list stubborn problem) for which the complexity is known to be quasipolynomial. Every partition problem for 4 nonempty parts and only external constraints is known to be polynomial with the exception of one problem (the 2K"2-partition problem) for which the complexity of the corresponding list problem is known to be NP-complete. The present paper considers external constraint 4 nonempty part sandwich problems. We extend the tools developed for polynomial solutions of recognition problems obtaining polynomial solutions for most corresponding sandwich versions. We extend the tools developed for NP-complete reductions of sandwich partition problems obtaining the classification into NP-complete for some external constraint 4 nonempty part sandwich problems. On the other hand and additionally, we propose a general strategy for defining polynomial reductions from the 2K"2-partition problem to several external constraint 4 nonempty part sandwich problems, defining a class of 2K"2-hard problems. Finally, we discuss the complexity of the Skew Partition Sandwich Problem.