摘要：We unify and extend previous kernelization techniques in sparse classes [Jochen Alber et al., 2004; Pilipczuk and Siebertz, 2018] by defining water lilies and show how they can be used in bounded expansion classes to construct linear bikernels for (r,c)-Dominating Set, (r,c)-Scattered Set, Total r-Domination, r-Roman Domination, and a problem we call (r,[λ,μ])-Domination (implying a bikernel for r-Perfect Code). At the cost of slightly changing the output graph class our bikernels can be turned into kernels. We also demonstrate how these constructions can be combined to create "multikernels", meaning graphs that represent kernels for multiple problems at once.
